" How does someone decide if someone they've just met who has had a few drinks is competent to mean the 'yes' they are saying, especially if they've had a few drinks too? "
Irrelevant to this scenario, as the man was sober (and had driven) whilst he stated that the woman was very drunk.
Separately: well, better teaching around capacity to consent is needed. Just as we expect someone pissed not to forget the law and get behind a wheel, and we are advised not to get in a car with someone who has been drinking in the driver seat, we should expect either or both pissed people to Not Have Sex if they are too pissed to judge their potential partners' consent.
Nothing bad happens if, on occasion when I sure, you don't have sex when it would've been ok to do so and just swap numbers instead.
You are running a risk that something bad can happen if you proceed. Whether that is legally rape or something that leaves one or both parties unhappy or uncomfortable. Or indeed, a contraceptive stuff up!
Are there people to whom something terrible happens, like genital explosion, if they don't have sex at every possible opportunity? No? Then, if you aren't crystal clear you have consent, stop.