I have a similar problem, haven't checked my vent yet though.

there are two toliets (devided by a wall, back to back) that I assume combine into a common drain. One toliet flushes fine although maybe a little slow. The other toilet is hit and miss. most of the time it won't flush anything, just slowly drains and sometimes not all the way.

I have used a couple of different snakes to try and unclog it. One is a crank kind and I'm able to get all of that in, but no luck. The other is just a long snake that you have to jam in by hand. I have got about 4 - 5 feet in the toilet, but no luck.

The toilet is about 20 years old I think.

 

degaylor1, Welcome to the DIY Forums.
If you used a 1/4 or 3/8" snake it is possible that it went through or around anything in the toilet trap. You need to use a Closet Auger. They are about 3 foot long with a curve on one end, covered with plastic to protect the toilet finish. They have a crank and a larget auger to clear the toilet.

In the future, please open a new post for your individual problem. Tagging on to another post can get confusing for whoever answers and sometimes the original poster. Thanks and good luck with your problem.

 

With a toilet that old, the most logical reason for poor flushing would be calcium/mineral deposits. Best bet would be to replace the toilet. Easy to do, very inexpensive.
B

 

Before I replaced a toilet, I would ream out the flush holes under the rim of the toilet bowl with a piece of coathanger wire. If that didin't work, you could pour a little diluted muratic acid in the tank and flush it through to dissolve the mineral deposits in the holes (IF that's the problem).
My two toilets are over 27 years old, and with a little minor maintenance from time to time, they both work like new.
Good Luck!
Mike