The scene where Riggs picks up Rika at the grocery store

It has, actually. There is one truth that has and will resonate throughout eternity - even the best line will fail if the girl doesn't like you, but, if she does, you can speak absolute garbage and she'll still go out with you.

What are you talking about? Mel Gibson was a girl's wet dream in those days. You still think it's the fucking LINES that do a pickup?

It only works because Rika & Riggs were clearly into each other from the first time they met

Now of COURSE "it's only a movie," but in real life a guy could theoretically pull a stunt like this, as long as he was able to read the signs and stop immediately once it's clear the woman's NOT into him

I think it's fine especially, as others have stated, she was totally flirting with him as well. Now, if she wasn't, then it'd be vastly different as well as her demeanor.