Your sentence is a contraction of this one:

It is a very funny movie, but there is a lot of tension and there are some touching scenes as well.

This means that you must say "there is a lot of tension..."; you cannot say "there are".

The problem can be avoided, however, by saying something like, ... but it also contains/has ...

for instance

Over the past few decades, I've noticed an increasing tendency for us Australians to say "there is" even with a plural noun. (At least I hadn't noticed this in my schooldays back in the 60s and early 70s.)

Everyone everywhere says "there's" with a plural noun, but over here in the UK I've never heard anyone say "there is" with a plural noun.

What matters here, however, is that a sentence that started *There are a lot of [+ singular noun] ... wouldn't be idiomatic, regardless of what followed. Come to think of it, I'm not sure that any sentence that started There are [+ singular noun] would be idiomatic.

I think you can certainly say 'there are' because the whole lot (tensions and scenes) add up to a plural. Having said which, I think few people *would* actually say that.

Everyone everywhere says "there's" with a plural noun, but over here in the UK I've never heard anyone say "there is" with a plural noun.

You're right - I meant the colloquial there's rather than there is.