Arguably Carrier, Bryant and Payne are one of the most well known brands outside of Lennox. Properly maintained, they're reliable and do the job of heating and cooling the home well. Not maintained, these furnaces can be a small nightmare. Trying to reach items like the flame sensor and ignitor require removal of the intake pipe and are still a huge pain. It literally takes me fifteen minutes to a half hour to remove and reinstall either. This isn't to say that other brands can't be a pain too, nor to besmirch Carrier or Nordyne (I have both brands on my house). However, there needs to a component of serviceability to equipment that customer and service technicians expect simplicity in. Goodman has excelled in this and Trane has gotten better over the years. Nordyne is also pretty easy to work on.
Another "problem" with Carrier, Bryant, Payne and Nordyne furnaces is one that's avoidable with proper maintenance, but few realize the importance or a good method of getting it done. Either way, the maintenance is neglected and the furnace suffers from nuisance shutdowns.
Now any furnace with a closed drain trap can suffer from this some problem. Nordyne is another one that comes to mind as does Trane. Amana and Goodman furnaces have open drain traps and unless the hoses are plugged are happy to run; soaking the surfaces underneath with water and possibly ruining them. Give Carrier and Nordyne credit on this one.
The drain trap is one of the most overlooked items on a furnace maintenance or service call, but just as important as an ignitor or flame sensor. If the furnace in question runs for a few minutes and then shuts down with a pressure switch error, pull the pressure switch line. If there's water in the line, then check the drain trap.
For Nordyne (Tappan, Frigidaire, Gibson or Miller), the trap is a "j" shaped piece of clear plastic in the blower compartment. If it's all loaded with crud, take it out and clean it. Cut the strips holding it and undo the clamps on the flexible lines. Take the trap to a sink and dump out the crud, but you may have to blow it out carefully to loosen it up. Put the trap back into furnace and make sure the hose isn't making a double trap that could be making the problem worse.
On Carrier furnaces, this will take a more creative approach. The hoses on older furnaces are likely rotten and easy to break. You need to advise the homeowner of the added cost or you're the one doing the work, make sure you have a replacement kit or you'll be without heat.
Remove the hoses from the top of the little barrel-shaped trap in the blower compartment. The pipe off to the side is likely glued on, so you can't remove it. The openings at the top are also different sizes. What you'll need is a bottle of water you can pour into the trap to help flush it out, a hose that will fit snugly on one of the openings about two feet long.
Pour some water into the trap and attach the hose to one of the spuds and put your thumb over the other. Blow into the tube, (don't suck or you'll get a mouthful of yummy water) until the blockage is out. Then you'll need to either drink some clean water and hold it into your mouth, or carefully pour it into the trap to flush it out. A gallon should be fine, depending on how long the drain is. If the drain is over two or three feet, you'll probably want to get a condensate pump. However, this is a much more expensive story.
Either way, make sure the drains and lines are clear and intact before you put everything back together. Run the furnace with the blower door open for a few minutes to check for leaks and you're done. Maranatha!