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
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")?