Perhaps I should amend that to "don't be obviously indiscriminate in a sleazy way". The bad thing isn't finding lots of people attractive, it's apparently caring nothing for them as a person (which is about having had no conversational interction with them before asking them out, some small amount of buildup is necessary, though as siduri says, if you're a decent chap, it's probably less than you think) or alternatively appearing desperate (which is about demeanor, I think). Things I've heard remarked upon have been bemusement at dinner invites following a dance with a stranger with no prior conversation, or demeanor problems.

If you actually like more than one person and have talked to the people concerned a bit, I don't see the harm.

(There's usually a niche for being the confident guy who flirts a lot with absolutely everyone: you get a name for yourself, but it's more as the loveable rogue than the creepy guy. That's possibly an advanced skill, though.)

Bonus link: only try these moves with a consenting partner ;-)

This has mostly frightened me off so far.

Don't let it. I actually disagree with the original advice for this reason: any benefit you get is likely to be outweighed by the additional anxiety from worrying what other people think.

My general take on this is the opposite: go ahead and ask many people if you're interested. Don't worry about what they think. Most of them won't care or mind anyway, as long as you're not rude or hostile about it. There's nothing wrong with asking out a lot of people.

In fact, this is a common internal obstacle to asking people out. A lot of guys seem to have the idea that it's somehow wrong or dirty to do so, as if they were being the bad guy by expressing interest in someone.