identify the errors in the sentences bellow and write the correct
form. explain the nature of the errors using grammatical terminology
where appropriate.
the play was very marvelous
we enjoyed very much our holiday
the play was very good. although it finished very late
despite we tried to book well in advance, we could not get tickets for the concert.
we musted to finishe our work before we could go out.
even though smoking is dangerous, however, it is popular.
the Thatcher's goverment was anti- European.
a car suffers if its engine is not serviced regularly.
tap water maeybe not pure enough to drink.

There are errors, but I would say that they are more in usage than in
strict grammar. For example, in the first sentence, "marvellous" is an
adjective, and therefore you should be able to say "very marvellous",
but it's unusual; "marvellous" on its own should be enough, or "quite
marvellous" if you really want to use emphasis.

My suggestions for the others: 

We enjoyed our holiday very much. (or We very much enjoyed our holiday.)

The play was very good, although it finished quite late. [This avoids
repeating "very".]

Despite trying to book well in advance, we could not get tickets for
the concert. (or Though we tried to book .....)
 
We must finish our work before we go out. ["must" is a verb, but is
used only in the present tense.]

Thatcher's government was anti-European. (Or "The Thatcher
government.....) You can use "Thatcher" as a possessive, which doesn't
require "The"; or adjectivally, which does; but not both.]

A car suffers etc is correct

Tap water may not be pure enough to drink. ["not" should go after
"may"; and there may also be confusion between the two words "may be",
and the one word "maybe" which means the same as "perhaps".

I'm not a gramarian, but I will give it a shot. Marvelous is already a
(perhaps)superlative word, so it is redundent to add very, besides it
sounds tacky.
Very much seems akward. I suggest "enjoyed our vacation greatly" or
move the very much to the end of the sentence. "We enjoyed our vaction
a lot" is less formal and common in the USA
Use a semicolen; instead of a period in the middle or "The play ended
quite late, but it was very good" The latter is more mainstream.
Few native born Americans would say it that way. The first part is
meaningless until you add "we could not get tickets for the concert" 
Much better is: "We could not get tickets for the concert, even though
we tried to book well in advance"
The next two should also be reversed. "We can go out after we finish
our work." Avoid "musted" and do not put an e on the end of finish in
the USA. Neither are in most dictionaries.
"Smoking is popular, but dangerous."
"Thatcher's government is anti European" or "The Thatcher government
is anti European."
Few Americans would infer a car can suffer. "Failure to service a car
regularly can cause costly repairs and poor performance."
Tap water may not be pure enough to drink. Maybe is  not correct
unless the sentance is positive (I think)    Neil