does this sentence make any sense...?

First-
An "amount" is a total number; therefore, it is erroneous to say "numerous" amounts -- as in more than one amount - when you are talking about one total (historical inaccuracies). For example, it would be okay to say, "The class members had numerous amounts of books. Sarah had five books (one amount), Tim had ten books (another amount), and Barbara had two (yet a third amount). You are talking about ONE amount - the number of historical inaccuracies in the film. There may be numerous inaccuracies, but there can be only one amount of historical inaccuracies, unless you break those amounts down by different categories.
Furthermore, "numerous" generally means "many" -- as in more than two. Therefore, "numerous" doesn't apply even if you are talking about TWO amounts - the amount of errors pertaining to historical inaccuracies AND the amount of errors pertaining to continuity errors.
Therefore, you should omit the words "amounts of".

Second-
If you intend the word "numerous" to apply to both types of errors (historical and continuity), you need no comma after "inaccuracies". If, however, by using the comma you were trying to indicate that there are numerous historical inaccuracies, but only a few (not numerous) continuity errors, you may keep the comma... but you need to clarify so that the use of the comma makes sense.

This leaves you with:
"...the film contains numerous historical inaccuracies and continuity errors."
or
"...the film contains numerous historical inaccuracies, and a few continuity errors."

... the film contains many historical inaccuracies and continuity errors.

I'd make it simpler and more clear. For example, "the film contains numerous historical errors."

You can't say "numerous amounts." You can have a large amount, or numerous examples.

"Continuity errors" is perfectly fine, but "numerous amounts" is bothersome. You can just say, "numerous historical inaccuracies and continuity errors." There should be no comma.