Yes, the comma there is incorrect.
What is correct depends on the intended meaning. Is the company secure, or are the translations secure?
If the company is secure, you should say, "Moscow Translations is a well-known, reliable, and secure translation company ..." That is, it is a company that produces translations that is well-known, reliable, and secure. (The comma after "reliable" is optional.)
If the translations are secure, then you'd say, "Moscow Translations is a well-known and reliable secure translation company ..." That is, it is a company that produces secure translations that is well-known and reliable.
Regardless of the intended meaning of "secure" here, you can't mix "well-known" and "reliable" with "translation". Yes, they are all being used as adjectives modifying "company", but "translation" is not the same kind of thing as "well-known" and "reliable". It is more "tightly bound" to "company" than the others.