When someone does something wrong, and you don't punish them for it, you can say that you "let it slide". For example, if you get caught for speeding by the police but they don't want to write you a ticket, they'll say:

All right, I'll let it slide this time.

(Or at least I imagine that's true, because it's never happened to me. I always end up getting the ticket...)

In the example above, the speaker obviously doesn't have the authority to punish his coworker for not going out to drinks, so saying "I'll let this one slide" is a joke.

You can use "let it slide" (when talking about a certain action) or "let this slide" (when talking about the overall situation). As you can see from the example at top, you can also say "let this one slide".