I like papers with big reference lists. Sometimes these citations lists are even more useful for me than papers themselves, since I can find some others papers. And this describes context and rises new questions for further work.
So since I like big reference lists in papers by others, I also try to include many references, 95% of them just "someone have done something related", and of course I do not read carefully such papers, just may be understanding what question has been asked and what is the context of this question.
However there are some (I remember 2) cases where I need to heavily rely on the results by others without deep checking the proofs (since it would cost too much effort).
I do not like doing so, but my experience says me that it should sometimes be done.
In general I think it much depends on the area you work, in my field it seems to me simple useful constructions are valuable, rather than complicated proofs.
I like what Igor Pak wrote here : Presenting work in progress
let me quote:
"For example, in Enumerative Combinatorics and Discrete Probability, two areas close to me, these priorities are sort of opposite. In the former, there are very few open problems. A nice new formula or a new bijection construction, even if only conjectured and checked by a computer, is already a lot of progress. Once you convince yourself that you can finish the proof, you can start giving talks - people will trust your judgement.
However, in Discrete Probability, there are lots of open problems and conjectures, often delicate and technically difficult. I would advise NOT to speak about your results until the proofs are fully written and carefully checked by somebody. This might work once or twice, but eventually there will be a seemingly trivial mistake which you overlooked in the first draft. Unfortunately, often enough such mistakes can completely destroy your proof."
So I think in the first type of areas deep checking is not relevant, but in the second it is very necessary. (In my (subsub)field situation is like 1, which makes my life more easy).