What's easier to say: "There's" or "There're"? It seems, increasingly, for many people it's the former. I've caught myself doing it. Example: "There's two ways to look at the problem." Don't contract, and you get: "There is two ways to look at the problem." That sounds terrible to my ears.

I think this is becoming common usage, to the point where most speakers don't even think it "sounds" wrong.

Here's a comparison done via google searches. (And assumedly, the comparison is even more extreme, as changes such as these appear in spoken English much earlier than written.)

"there's two" - 105,000 results >>>>>>>>> "there're two" - 5,980 results
"there's three" - 37,000 results >>>>>>>>> "there're three" - 1,710 results
"there's four" - 15,900 results >>>>>>>>>"there're four" - 4,620 results

Here's a long, and interesting, discussion, if you're interested in this sort of thing.
[snip]
What _has_ happened is that some nouns once indubitably singular
have recently acquired a plural sense, sometimes as a shadow
double and sometimes almost to the exclusion of the original
singularity..."Lot", for example, is now singular only when distinctly and
obviously referring to a collection as a single unit, typically
in commercial contexts...
[snip]