Don:
Lots of good ideas have been mentioned. Several items need to be nailed down, however.
(1) System Ground - is the main panel grounded according to Code requirements? There should be a ground rod (with rare exceptions) driven eight feet into the ground with a preferably solid bare copper wire properly attatched leading into either your meter box or your main panel. It should be firmly attached to the ground bar on either panel. You can tell which is a ground bar by determining whether or not it has a direct metal-to-metal connection (proper term: is bonded to) the metal panel box itself. This can be a screw or a metal jumper, etc. There should also be a similar bare wire copper bond to the cold water piping in the house if the piping is predominantly metal.
(2) Bonded Neutral - this is trickier to describe in generalities. At some point, probably in your panel, your main neutral bus will be bonded to your ground bus. This is very important. There is also an important neutral grounding/bonding procedure which must occur at the transformer on the pole. It can and does happen that these connections fail over time, and it is not unreasonable for you to insist that your utility company come out and thoroughly check the transformer, its outputs, and all its connections thoroughly, even to the point of putting recording meters on the transformers for a time. If they refuse to do this, do not hesitate to contact whatever regulatory board is responsible for their oversight.
(3) Main Bus/Breaker - your letter did not specifically mention how the main bus was fed. This area is my site of greatest suspicion, given that problems occur in some parts of the house and not others. If the panel is a simple bus, one side may have a defective/failing/degrading connector or connection where the main comes in. You would not be able to completely determine this simply by "wiggling" the wires. An infrared thermometer might detect this, or actual inspection behind the bus by disassembly after pulling the meter (licensed electrician needed here). If the panel is a main breaker type, again one side may be failing; here we go with the infrared thermometer and the disassembly, etc. But you see my point - if only one bus is momentarily shorting inside an old main breaker, you could get unusual high and low voltage-appearing symptoms in only portions of the house intermittently. I have seen several instances where old main breakers did not fail safe.
(4) Scary thought - in old systems, it can be combinations of the above - and more. The reason I say this is that some panels split the neutral bar as well, thus introducing the possibility, albeit remote, that one side has loosened. If your panel has a split neutral, check this as well.
By the way, a 100 amp service is woefully inadequate if your brother-in-law upgrades appliances, adds new ones, etc. If parts in the old panel had to be replaced because they were "rusty", LOSE this panel and upgrade to a 200 amp panel. I am betting your problems would vanish. If you are still worried about the state of the utility feed, insist on the recording meters on the utility side. Seriously, Don, you guys can spend a lot of time (and money) chasing these problems around on a creaky old panel. The real problem is that, in the meantime, if your brother-in-law has computers or other sensitive electronics at home he can screw these up big time before finally succumbing to the obvious and bringing his physical plant up to spec.
Hope this helps!