I am a non-native English speaker and I recently started noticing that most people do not do the correct agreement of the verb with the noun when saying "there is"/"there was"/"here is". They say, for example,

There's two things in my pocket

instead of

There are two things in my pocket

as it should be. In discussing this issue in two distinct occasions I was asked whether the word "heaps" also should be preceded by the plural form of the verb (and the same for "lots"). I could not answer it, but I think the answer depends on whether the noun is countable or not. So, for example, I could say

There are heaps of glasses on the table.
There is a heap of glasses on the table.

but if the noun is uncountable, I am not so sure. I would think that the only correct option is to say

There is a lot/heap of water in the glass

but native speakers say

There is lots of water in the glass

Is the latter correct in terms of usage ("lots of"/"heaps of" + uncountable noun) and in terms of verb agreement ("there is" + "lots"/"heaps")?

I am a non-native English speaker and I recently started noticing that most people do not do the correct agreement of the verb with the noun when saying "there is"/"there was"/"here is". They say, for example,

There's two things in my pocket

instead of

There are two things in my pocket

as it should be. In discussing this issue in two distinct occasions I was asked whether the word "heaps" also should be preceded by the plural form of the verb (and the same for "lots"). I could not answer it, but I think the answer depends on whether the noun is countable or not. So, for example, I could say

There are heaps of glasses on the table.
There is a heap of glasses on the table.

but if the noun is uncountable, I am not so sure. I would think that the only correct option is to say

There is a lot/heap of water in the glass

but native speakers say

There is lots of water in the glass

Is the latter correct in terms of usage ("lots of"/"heaps of" + uncountable noun) and in terms of verb agreement ("there is" + "lots"/"heaps")?