Plenty of potential problems can come up when you install a new plastic laminate countertop on top of an old one. It's not because the job is so difficult--it's actually relatively easy, once you master a few basic skills--but because it's not nearly as simple as it seems. If you fall into the trap of believing there's nothing to gluing one piece of flexible plastic on top of another, you are almost certain to wind up disappointed.
The wall behind your countertops almost certainly looks flat, but is it really? Often the answer to this is "no." Use a carpenter's square to test the wall's flatness. If you notice some uneven spots, put a piece of masking tape on the back of the counter at the base of the wall. Use a scribing tool to scribe the shape of the wall onto the masking tape, then remove the masking tape and stick it to the front of the counter or the floor, someplace where you can get a good close look at it. Ask yourself if, cutting freehand, you are able to perfectly cut along that scribed line. If not, be aware that you have to remove the countertop from the cabinets so that you can use a router to shape the laminate's back edge after you attach it to the countertop. This makes the job much bigger.
If your existing laminate is showing its age, there's a decent chance that wood underneath is as well. If water has found its way through any seams or cracks, the wood underneath may be warped. Use a straight edge to see if your counters are perfectly level. Also be on the lookout for any soft spots that show the counters underneath may have been compromised and may need to be replaced.
Installing a new piece of laminate on top of an old one that is coming loose is like putting a new tire on a bent wheel. Make sure you've got good adhesion by tapping the entire surface of your countertop. If you hear any telltale "pops," then you either need to remove the existing laminate, or screw a quarter-inch piece of plywood over the entire countertop. Either solution adds considerably to the scale of the project.
Remember that plastic laminate is flexible--even after you glue it down. If your existing laminate has a lot of chips or deep scratches, over time these become visible in the new surface. Minor scratches are no big deal, since you have to sand the entire counter by hand to prepare it for the adhesive. If a simple hand sanding won't be sufficient to smooth the countertop, you need to remove the old laminate or cover it with thin plywood.
Putting new laminate on your countertops can be an incredibly cost-effective way to brighten up your kitchen, but look before you leap. A lot of hidden factors can cause your hard work to yield very mediocre results.