Got 700c 23mm tires on my bike, they're slick and I'm guessing more for racing than commuting, so I already caught 3 pin-hole sized flats from bits of glass. What would you guys suggest to remedy this? Slime? A tire with more tread? What about using those solid-rubber, airless tires? Ride isn't THAT smooth over rougher terrain, so I figure it shouldn't get much worse, and I'm used to skateboard wheels and how solids generally feel.

Tuffy tire liners. people say they will put a hole in a tube too, which, IME, is correct, but they'll prevent 10 to every one they create.

Tires with a flat protection layer. Some ride nice (Continental GP4000). Some do not. Less air pressure may help too, with 25mm tires allowing lower pressure especially if you weigh much over 150 pounds. If that doesn't work you can use tire liners which will not ride nice.

Use quality tires with a Kevlar-type inner cords lining.
Have successfully used Maxxis Re-Fuse tires; last year a total of 5,000 miles of riding and 2 flats beween our tandem and my single bike.
One was a puncture from a tiny piece of steel wire from radial car tires and the other was a patch that came loose.
Live in the desert southwest, so lots of debris, cactus needles and a few goatheads + the usual road debris.
Tested solid 'airless tires' decades ago for a company. NO thanks! On super smooth roads no issues; bumpy /rougher roads lots of road vibration and crossing a cattle guard (if you live out west you know what those are) it actualy made the bike shudder.
Slime? Tried it years ago and not worth the bother/$$; it can mess up your valve stem and it may only seal some of the smallest of holes. Then if you do get a real flat the slime/goop is all over inside the actual tire and a mess; almost impossible to patch the tube too.
More thread is not necessarily the answer either, as debris can get stuck in the tire grooves and create a puncture.
Watch where you ride or even use old fashioned tire savers. And carry a spare tube and pump.
Just our experience in over 300,000 miles of riding.
Rudy/zonatandem

Some tires are noted for flat resistance, some are not, sounds like time to go for more flat resistance. Continental Gatorskins, for example.

The slickness isn't an issue for flat resistance, but thickness and toughness of the tire is. The Gatorskins are still basically slicks on the tread part.

I see. Guess shopping time early next week not to have to deal w/ this nonsense. Only in the rear too, so I'll give front more time to luck out.