Before you buy any used car, check its model year's reliability. Honda made that Accord model from 2003-2007. Just type in... reliability of the 2003-2007 Honda Accord. It will take you to websites that will give you the trouble spots on some of the cars made. So zero in on those trouble spots when you are out shopping for a used car. Avoid cars with those issues, or if you plan to have those items fixed, get a reduced price on the car.
Also, Honda has been making 4 cylinder vehicles for a while now, so I would stick with that engine and trans combination. But oil changes and coolant flushes are a must with that small engine.
Was it used for urban commutes? In bumper to bumper gridlock, that transmission can shift hundreds of times over several miles... then figure that daily grind over ten years. That's a lot of shifts that may not always show in odometer miles. Visualize a cab in New York City in the heat of July taking a half hour to go a mile or two. One red light after another up to about third gear, then back to zero, and over and over and over. Or the car you bought on a freeway near you! Conversely a car that goes long distances with no shifts may have high miles but low transmission wear.
124,000 is lots of miles for stop and go traffic, especially in high temperature areas, and think of how many times that transmission has shifted in those 10 plus years? If the previous owner never had the fluid changed and neglected similar things, I wouldn't blame the manufacturer for it. If in doubt or if those gadgets under the hood pose a mystery, then a quick look-over by a trusted mechanic should be part of any used vehicle purchase.
Unfortunately, those were the dark years for the Honda Corporation and its automatic transmissions (V6-auto / 1998-2004). A friend of mine has owned a transmission shop in my home town since the mid-50's (family run, father/son venture). Approximately two years ago, I was speaking to him and expressed an interest in the 2003 Honda Odyssey. I couldn't believe how 'bargain-priced' they were in my area. He told me flat-out to stay away from them. The transmissions in those vans (5 speed /automatic) were very problematic and could not be rebuilt. When they went, his shop had to order a new one from Honda Canada at a cost of $3500/each. Their greatest failing was that they overheat and literally cook themselves. A transmission cooler would likely prevent the problem; however, unless the original owner took that precautionary step shortly after purchase, the odds were against you in the used car market.
I have owned Honda's for several years, but tend to focus on the 1994-1997 Accord line-up. They tend to be bulletproof (engine & drivetrain). An excellent resource for used cars in Canada is a book called "Lemon-aid", by the author Phil Edmundston. He has been reviewing new & used cars since the late 60's / early 70's. It is highly recommended reading!