The dim screen could be either a failing tube, a fault on the driver board, or a problem with the LCD shutter which sits in front of the CRT. There is a fairly easily accessible brightness pot inside the scope, accessible through a hole in the metalwork on the CRT side near the front. You just need to slide the outer cover back by a few inches to expose it.
As for the offset, this is more than likely a result of the leaky capacitor problem that this range suffers from. There are surface mount electrolytic caps on all the boards (acquisition, logic and front panel) which leak corrosive electrolyte onto the PCB. You'll need to remove them all, carefully to avoid lifting pads, then clean the board very thoroughly with a suitable solvent. If you're lucky, simply replacing all the caps with new ones will fix the problem. If not, you'll need to look around for components or PCB tracks & vias which have corroded, and perform whatever repairs are necessary.
The acquisition board is usually worst affected, since there are are more caps on this board than on the logic board, and they're closer to other components which can be damaged. Go round the whole of this board with a camera and photograph everything close-up before doing anything, you may well want to refer back to see which caps went where and what condition various parts are in.
The good news is that many of the components on this board are actually fairly generic op-amps and 74 series logic, which can be replaced as needed at minimal cost. Although there are some much bigger, unobtainable components too, they're generally located far enough away from the caps to avoid damage.
If you're lucky, you've got yourself a very good scope indeed at a bargain price. If not, I'm afraid it's a rather bulky paperweight - but still one which you might be able to break for parts and sell for spares once you've identified which bits are good and which are dead.