UPS to fix dimming lights due to laser printer?

I think you would be better off fixing the problem. All electrical devices consume some power, therefore adding a UPS will provide a source of power when the input is lost or drops too low, but in being on will make your situation worse. That is because MORE current will be consumed than that of just the printer.
If lights are dimming when this device is running, there is a voltage drop that is occurring on the AC lines. Most often this is due to a high resistance path in your electrical wiring. Poor connections, too small gauge wire, and possibly limited AC input service (although this is probably the least likely) could be responsible. You should get someone qualified such as an electrician to take some measurements.
For what it is worth, aluminum wiring is famous for this type of problem.

DImming lights don't always mean there is a problem with the wiring, althought they could. Given that the only other problem is the hair drier, It is more likely that the dimming is just due to normal voltage drop. It only takes a few volts to cause noticeable flicker, which could be well within the acceptable voltage range. A laser printer pulls high current peaks which cause this. Every recommendation you will find calls for a dedicated circuit for the LP, which would minimize this problem. I agree, however, that having someone inspect it is the only way to know for sure.
Ben Miller

There are subtle factors about wiring that may contribute to your "dimming lights" problem.
1. Loose connections - age, sloppy orginal work, whatever... may have an effect on voltage drop in the outlets themselves. Carefully turn off the power at the main breaker/fuse box and make sure all of the wire connecting screws on the outlets are tight. Splices with wire nuts must also be tight.
2. Most likely cause - overloaded circuits - or circuits near capacity. It is not difficult to overload a 15 amp circuit. The more active appliances and lights on the line, the greater the voltage drop. Thus when your printer calls for 450 watts of additional power, the voltage is going to drop on the whole circuit, causing the lights to dim.
20A circuits are better than 15 amp circuits (because if they were installed correctly, the wire is larger and can handle more current)... thus... less voltage drop for a given load. Of course, you may only have 20A circuits wired for you kitchen appliances (or not at all, if your house is really old). Bottom line, if you can... move your printer to a 20A circuit or install a 20A circuit for the printer.
3. Long circuits - The longer the distance your outlet is from your breaker/fuse box, the greater will be the voltage drop. If you have any control over this, try to keep this distance as short as possible.
4. Under capacity service entrance/fuse box. You say the dimming problems happens on multiple outlets throughout the house. Are they, in fact, on different circuits? If so, your service entrance/fuse box may be under-capacity. In the 1950's... 60A was common for apartments and old houses. 100A for newer houses.
In the year 2007, that is no longer enough for most houses, because many things used today (dishwashers, air-conditioners, computers, laser printers, central vacuums, etc.) weren't all that commonplace during the 1950's. 200 Amp is the minimum, in most cases.
Upgrading the service/fuse box to your house is the most expensive fix. It may also involve running new circuits and wiring to your appliances.
Beachcomber

You've most likely got problems with your wiring. A high resistance joint is not only annoying, but also can be a real fire hazard. A very slight flicker can happen, but a noticeable sag of any duration is not acceptable. I recently had that problem and I actually had to have the utlity company over twice before they took care of a burnt splice out on the pole. If that splice had been inside, it likely would have lit the house up. It was actually burnt, not just warmed. One thing you might try is getting a chunk of romex and hooking it directly into your panel and bring it inside like an extension cord and run that machine on it as a test. If it doesn't sag the rest of the house hooked like that, then you need to look through the circuit it was on, and probably the whole house. If it still sags, it's somewhere farther up the line, maybe the utlity companie's conductors, or the meter socket etc.