Would it be a bad idea to ride a 700c wheel on back, and a 27 1 1/4 wheel in front?
I know there's an 8mm difference in diameter, but I'm trying to make a cheap commuter that I can also train with a little. (fixed gear to practice a more round and continuous stroke)
I'll be riding this on short trips. like 5 miles at the most.
Someone's selling a 700c flip flop hub rear wheel, but no front wheel.

You'll have to adjust one brake, and it may or may not be possible to do so depending on the brake reach. The only other downside is not being able to swap tires around, so if you wanted to carry a spare you'd need two. The tubes are pretty much interchangeable.

Oh, and since the front will be higher than the rear, you'll always be riding uphill.

I very much doubt it'll make a difference, I managed to ride an old Raleigh with a 26" front wheel and a 700c rear for quite a while (it had drum brakes) without anything untoward happening. Lowering the rear end by 4mm will make virtually no difference to the geometry.

alright, thanks all!
Although a little after posting this, I found an ad for someone selling a wheelset for not too much more. (the rear wheel alone was $35, the set is 70)
Plus I like the gearing on the set better. 15t freewheel/17t fixed vs 16t freewheel and 19 fixed. I have to check my brakes to see if I can lower them a few mm though.

Is this a road bike to fixie conversion? The frame that you'll be using, was it intended for 700 wheels? Not that fitting 700 wheels on a frame intended for 27" won't work but you could increase the chances of pedal strike when taking a corner at a good clip... something that isn't much fun when riding fixed. This is what many people doing fixie conversions don't think about and it gets even riskier when using road cranks with 170mm or longer crank arms instead of track cranks.

Is the 4mm difference going to matter that much?

as long as the brake shoes hit the rim fully , with out being half in the air or into the tire
Its all good.

It can mean the difference between washing out the rear in a turn and kissing pavement or barely scraping and scaring the crap out of you. Are you using 165mm track cranks? If not, add at least an additional 5mm in clearance reduction... maybe more since road cranks can also stick out from the frame a little more than track cranks since they normally have 2 chainrings... at an angle that reduces clearance even more.

I'm not trying to talk you out of a conversion, it's what I learned to ride fixed on almost 30 years ago, just saying you need to be more aware of corner speeds (therefore your lean angle) somewhat.

Since you're using a flip-flop, ride your bike as a SS for awhile and remember to pedal through corners to see if you have the clearance to go fixed. If you ever touch down, you at least have a better chance of not wiping out since the ability to back-pedal may reduce the force of the pedal hitting the ground thereby lifting your rear wheel.