In your shoes I'd do what alavahalf did, just make sure you switch things off before jamming a screwdriver into them.
You probably can tell high power from low, most items have the "wattage" written on the back. Failing that, the higher the fuse current in the plug, the higher the power the device takes.
Interesting one, it's the sort of question I feel I ought to be able to answer, but I'm unsure what it is. Dimming lights suggest the power wasn't available for a short while. i.e. turning on the appliance caused a surge to it, and robbed power from those items already on. But if we aren't talking freezers or ovens and such like, then it's difficult to see why it would happen.
Yes best to ensure everything is tightened, and if that fails to cure it, get an electrician in to check out the fusebox/RCD etc.