Should they be avoided? No. Just as queer was taken as very derogatory by homosexuals and was "reclaimed" by the homosexual community, English speakers should reclaim their right to use gay and queer in non-homosexual contexts. They should be able to utter a phrase like, "Come with me and let us gayly prance along the promenade" without anyone looking at them queerly. However, in practise you can more likely use queer with its non-sexual meaning than you can use gay simply because gay is far and away the more common of the words. Queer is far less popularly used to refer to homosexuality so the association is much less strong.
Your question is quite broad as there are a multitude of words so I'm going to stop at 20 as they come to mind. (I've just counted 21, and a few are multiple related words, but that's fair enough.)
Faggot is an uncommon term now that people aren't so much gathering their own wood to burn. It is (sadly) known almost only as a very insulting word for homosexuals whereas it used to mean only a bundle of sticks tied together for burning. It is often shortened to fag, also insulting, but that word can also mean cigarette.
Erection is seldom used to mean "a tall structure or building" nowadays and instead people will more quickly associate it with an erect penis or, much less often, clitoris. Be prepared for odd looks if walking past Nelson's Column (a monument in London) you say loudly, "Look at Nelson's big erection."
Sphincter means "a ring of muscles used to open or close a bodily orifice". Due to the anus having a sphincter that is its most common understanding. This is despite the beautiful saying "the eye is the window to the soul" when two lovers stare into each others' pupillary sphincter (the ring of muscle that opens and closes the pupil). Chances are you won't want to use the word often outside of a medical or biological context but if you happen to be a marine biologist talking to a bunch of non-marine biologists the term might arise.
Retard/retarded/retardation. It means "to slow down, to delay". This one very much depends upon context. The general public unfortunately only associates it with "mental retardation". That term has itself fallen out of favour even amongst those in the mental development field. Calling someone with a mental handicap a retard is apparently so highly offensive that a popular song called "let's get retarded in here", meaning to have a very energetic party, was heavily criticised in the USA. It was re-recorded with the lyrics changed to "let's get it started in here". In a (non-neuorological/non-biological) scientific context retard is still used. Since the word is of Latin origin Romance languages actually use "retard" to mean "slow down" without the prejudice it has in English.
Mongoloid. This means "someone who looks like a mongol", that is, someone of East Asian ancestry. The term was adopted in the early 19th century as part of a "three races" theory of humanity: there are negroids who were named for their dark skin, and caucasoids, though often called caucasians, who were fair-skinned. The term is still sometimes, but uncommonly, used in anthropology as the theory has fallen out of favour. During the late 19th century Dr Down adopted the term for people with a certain mental disability as they shared some facial features with East Asians. During the mid 20th century the term was disapproved of and largely replaced by "Down's Syndrome" but some people are still familiar with the mongoloid term, it can still be found in books from that era, and are highly offended as they are unaware of its meaning in anthropology.
Fanny is now common in the USA where it means "bottom, buttocks" and is used widely in the term "fanny pack" meaning a small bag worn on a belt that usually rests on the top of the buttocks. However, in Britain/Australia/NZ fanny still means "pudendum, external female genitals" though outside Britain it is largely being supplanted by the US meaning. "Bum bag" (bum is slang for "bottom, buttocks") is a name for the bag used when fanny is used for genitals. Fanny is also a proper female name, though it is very, very rare to meet a woman called Fanny and it's mainly encountered in dramas or books set in the Victorian or Edwardian era (19th through to early 20th century).
Negro. It was a very proper and polite word that was used by the public and by anthropologists in reference to people of dark-skinned genetic origin. But in the USA a few decades ago it was decided that it was offensive. Nowadays even if you're talking about some rivers (each called Rio Negro) in South America the word will stand out. The term is less offensive outside of the USA.
Cock is the proper name for a male chicken and for many species of birds, particularly the Galliformes (chickens, turkeys, pheasants, etc.). Sometimes "cockerel" is used, but most people say "rooster" and if you say "cock" they will think of "penis". Many times is told the suggestive joke "look at my big black cock" when referring to a bird.
Pussy is an affectionate or childish term for a cat. While "pussycat" is fairly common, use of the bare term "pussy" is very commonly associated only with pudendum or vagina and used in that way is considered vulgar. Again, many suggestive jokes are made about "come stroke my pussy".
Dumb means "mute" as in someone or something that can't talk. It's nowadays used to mean "stupid, lacking in intelligence" and when people say "dumb animal" they no longer mean an animal that can't talk but are implying the animal lacks intelligence. Calling a human "dumb" used to mean they person couldn't talk. Nowadays it is taken to mean stupid. Calling someone who can't talk "dumb", especially someone who is "deaf and dumb" (can't hear, can't talk) is grievously insulting for some reason despite it being only a few decades ago an accurate description.
Dwarf/Midget. Used to mean a short person who had the condition "dwarfism" so even when fully grown was much shorter than the normal height for a human adult. Now the preferred term is not midget (which is almost always offensive) and often not dwarf (which may be a preferred term); "little person" or "person of short stature" are likely acceptable.
Abnormal. Abnormal means "not normal". In terms of height a little person is abnormal as is a giant who has giantism/gigantism. Height is the defining characteristic of those conditions. But if you call such a person abnormal you're generally considered rude and discriminatory even if you are completely accurate and you have the statistics to back it. The same holds true for describing anyone with any trait outside the normal range as abnormal. Saying "you are abnormal (because you have extra fingers)" is often seen as different to saying "you have an abnormal number of fingers" though people may still take offense at the latter. It's okay to describe things like medical test results, a spider web spun in micro-gravity (commonly called "zero-G" or "space"), two headed animals as abnormal but people get really fussy when you call them abnormal.
Oriental. Foretting that in antiquity "the Orient" meant Asia Minor and what we now call the "Middle East", in modern speech oriental/Oriental used to be the proper general term for anything to do with the Far East/Far Eastern Asia (Japan, Korea, China, Thailand, Vietnam etc). Nowadays you can say you "want to eat oriental food" but to call a person from the Far Orient an "Oriental" is sometimes going to cause offense. Often the preferred term is Asia/Asian. However, in Britain Asian refers to people of Indian/Pakistani/Bangaldeshi/Nepalese and similar origin; despite the shared genetic heritage making them appear largely identical, Pakistanis in particular find it offensive to be called Indian. "Chinaman" is now a practically unheard term and is considered offensive despite it being the polite term several decades ago.
Indian when referring to someone from India is entirely okay. When referring to a Native American it's offensive.
Half-breed/half-caste/mulatto. All referring to people of whose parents were (usually visually) of mixed-race heritage. Mixed-race is acceptable.
Yank, while slang and so strictly not something you wanted, is very, very commonly used by native English speakers outside the USA to refer to anyone from the USA. Some USA people find it offensive due to a war they fought betwixt themselves 150 years ago where one side called the other "Yankees"; however "Yankees" themselves like that term enough to use it as a name for a major sport teams.
American/North American may cause offense to anyone living on the American continents if used without intending to include them. Mexico is in the continent of North America and I vaguely recall some news articles some years ago that mentioned offense at Mexico not being recognised as included in "North American". While South America could technically be covered by the term American, in popular practise the term only refers to people from the USA (including people from Hawaii though the islands are not part of the continent) and I don't recall hearing that any South American was aggrieved by not being referred to as American.
Wench meant simply "child" and then it changed to "female child" and then it came to mean "young woman" and "serving woman". Similarly "boy" often referred to a male servant (much as garçon is used in the French). But it's now considered offensive to call a servant/waiter "boy" and wench is also considered a diminutive. Wench also has (undesired) connotations of sexual promiscuity or prostitution and "to wench" means to seek the services of female prostitutes.
Rubber is generally polite in British English and its closer relatives where it means "a device for rubbing out pencil marks". However, in AmE it refers to a condom and that meaning is becoming ever more common in BrE.
Ejaculate means "to utter quickly" and an ejaculation was the very short speech when one ejaculated. It also shared meaning with the term "interjection". However, nowadays it's really only understood by most people as the "ejection of liquids accompanying sexual orgasm".
Intercourse is really only understood as "sexual intercourse" -- which you'll see is constructed as a noun preceded by an adjective to indicate it is a sub-type of intercourse -- not as any social interaction. The more specific meaning has supplanted the more general meaning so be wary of with whom you claim to have had intercourse.