The signs and symptoms of a bad and failing automatic transmission is taking too long to shift, the RPM's going up but vehicle doesn't gain speed, burn transmission fluid, transmission slipping, whining or clunking noise.
If you notice that your vehicle takes more than a few minutes to shift into the next gear while accelerating then either your transmission fluid is low or you have a clogged transmission filter or the transmission is about to go out.
The transmission when it's working properly should respond within a few seconds to the changing of gears upon acceleration.
So it should almost immediately shit up into the next gear when you accelerate and the RPM's go up and if not something is not right.
Sometimes it's as simple as low transmission fluid, dirty transmission fluid or clogged transmission filter.
Then other times it could be the automatic transmission going out.
If it's a manual transmission then the gears could be grinding when you try to shift it or you notice clunking or grinding gear sounds when accelerating.
If you have a transmission temperature gauge and it goes up way too high then you have a transmission problem that needs checked out.
An automatic transmission should last 160,000 to 300,000 miles and sometimes more depending on how well you care for it.