Bicycle Mechanics - Keep Getting Flats!!

I bought a new rear wheel for my singlespeed trek 400, 622x16, which should fit 700x25 tires just fine. I'm running the original front wheel on it, which hasn't been a problem at all. When installing tires on the new rear wheel, I've noticed it is very easy, a little too easy, almost effortless. I can take the tire on/off with no levers. When fully inflated, it cinches up well and all seems copacetic. I've replaced the tube twice now, and it has happened the same way both times... I replace/patch the tube, ride on it for most of the day, come down the next morning or a couple hours later and its flat! The holes seem to be in roughly the same place on the inside of the tube, but I can't find anything on the inside of the new rim that could be puncturing it. Now basically what I am asking is if you think this is an issue of my rear rim being too small/rear tire being too big.
Please help! Its driving me NUCKIN FUTS!
Thanks.

Check the rim-strip in the area of the hole. Feel around the edge of the hole in the rim for sharp-edges. Also make sure there's not a spoke that's too long and is poking through the rim-strip. Replace with Velox tape wide enough to cover the holes in the rim completely.

Before cooling for a complicated reason follow Danno's advice and check the rim and tire carefully in the area that your punctures are occuring. Also learn to make a reference mark on the tire at the valve (or mount with a label lined up), so you can quickly line the tire and tube to check for possible causes.

If you can't find any burrs, exposed spoke holes, or rough spots it might be a narrow rim issue, though it's odd that your problems occur in the same place (unless you mean on the belly side generally)

One problem of super narrow rims is that the inner walls of the tire come close together forming a space that's sort of an hourglass shape in cross section. When the tube is inflated it first fills the tire section, then with friction holding it against the walls of the tire, the small section stretched across the gap blows out like a bubble and fills the section in the rim. (Draw yourself a small x-section sketch if you can't visualize it)

As a result the tube material stretches 2-4 times more in that narrow zone than anywhere else and is prone to being over stretched and failing. It's especially a problem if you installed the tube with a twist.

There's no sure cure, but here are a few hints.

1- Buy decent quality tubes, they're more uniformly made, and less likely to fail from overstretching. You don't have to go first class, but try to stick with decent brand name tubes like Kenda, or IRC, as opposed to house brands or even bike company brands. Manufacturers are more likely to pay attention to quality when their own name is on the box.

2- buy the right size tube, preferably the largest width that's less than the tire. ie for your 25mm tires a 23mm tube is a better bet than a 20mm
3- inflate the tube to a sausage shape and rub it liberally with talc which will help it slide within the tire.
4- stuff the sausage well up into the tire avoiding twists and stretched or bunched zones
5- mount the tire, letting enough air of the tube to make the job easy, but not enough for it to lose it's sausage shape.
6- finish by pushing the valve up into the tire taking any part of the tube that may be trapped under the tire, then pulling it fully down to the rim, working it's base past the tight spot.

Starting with decent tubes, and installing them carefully, you should be able to put this behind you for good and get flatsm in the tread area like the rest of us.

good question is what does the puncture look like? (pin hole, snake bike, long slice, large-muli tare look)

the punctures are small slits, about a cm long. I've been using 18-23mm kenda tubes, and there don't seem to be any sharp bits on the inside of the rim but I'll install another extra carefully. Thanks for all the info!

Sounds like an improper installation to me. Double punctures would indicate too low a pressure, but you are indicating a single puncture. A slit like that probably means the tube is getting stuck between the rim and the bead of the tire somewhere.