What is the difference between "should" and "must"?
e.g. "They should have called the police." Can I use "must" in that sentence or not?
e.g. "You should read his new book." How about this sentence?
To answer your first question 'must' is possible in the above example but the meaning will be different than i suppose you have in your mind
When we use 'should' we think what is right/moral/decent thing to do at the time.
When you say 'They should have called the police.' - (Here you know it for sure that police have not been called)
But when you say 'They must have called the police.' (Here you are almost instinctively sure that the police had been called after you have anaylzed the situation well, but officially you don't know whether they called the police or not)
See below how 'should' and 'must' function in your examples
They should have called the police. (It is your opinion)
They must have called the police. (It is your speculation)
But when you know that they didn't call the police in this situation then you might express your surprise in the following sentence
Suppse you are telling your friend the following
Here 'must' is not possible - because you can't compel your friend to share things with you. Sharing is not compulsion. So you can't say --
You must share your problems / feelings with others.
But you say --
You should share your problems / feelings with others.
'Must' in one of its meanings implies compulsion, obligation etc.
To answer your second question -
You should read his new book. (Sounds less convicing than 'must' but it is still a suggestion)
Here 'should' works as a suggestion But You must read his new book. (sounds more convicing)
If there is any book or movie that you have liked very very much then you use 'must' not should. 'Must' will work as 'strongly recommended'
So it should be
You must read his new book. It's amazing.
Should are Must have different meanings and each with various common usages. In your example, "should have called" means an action did not occur that you would have liked to have occurred.
Also, in your sentence, if you have "must have called", it represents a conclusion to explain a past event.
This usage is not related to a decision of using "should" versus "must".
"I got mugged last week." "Did you call the police? You should have called the police." "I just got mugged." "You must call the police!"
In your examples, "should" represents a suggestion for action, while "must" represents a command where you want the listener to obey you.
Often "should" is used instead of a direct request. "Please pick up your clothes from off of the floor." "You should pick up your clothes from off of the floor." "You must pick up your clothes from off of the floor."