http://www.txdps.state.tx.us/vi/index.htm
Dallas is still part of a dual testing program. They will plug in to your OBD or on board diagnostics as well as do a tail pipe test on any vehicle more than 2 years old.
There are certain waivers that can be granted such as low income and extended grace periods are allowed in some circumstances.
Starting with 1968 vehicles, a visual inspection of the required emissions systems on the car will be checked regardless of antique classification.
If you get stopped and the inspection sticker is checked for validity, you will wish you had invested the money to have the vehicle repaired and legitimately pass an inspection. As some have mentioned, there are inexpensive items that can cause a failure.
I am not as versed on passenger vehicles as I once was but do have my current inspector certification that I use solely for inspecting semi trailers for a manufacturer/repair company.
If you have a sticker from any of the counties that require emissions testing on your windshield and you attempt to get an inspection in a non emissions testing county, you will be asked for proof of residency. Either your drivers license or a utility bill will suffice. If you claim you just moved and don't have your first bill and haven't changed your drivers license, you will be required to sign an official form stating that you are in fact a resident of the county in which you are seeking inspection.