Well, we had several contractors come out to look at my mom's basement to see what might be going on. According to our tenants, water has been coming in at a steady rate since last week. They've been nice enough to keep sweeping it towards the sump pump pit, but I know it's a huge hassle for them and not something they wanted to tackle right after moving in. To complicate things, one of the two sump pumps--located at either end of the basement--just burned out.
The general consensus is that with the record rains we've had the last few years, the water table in the area has risen. There has been an increase in the number of basements taking on water The neighbors on either side of mom's house are currently dry, but her house does sit a little lower.
The seepage is coming from the cove joints, where wall and floor meet, as well as from a few cracks in the floor slab, common symptoms of hydrostatic pressure. Basically, the water table is trying to equalize itself from the exterior walls to the inside of the basement. We need an interior footing drain tile system. This will relieve the pressure, and channel the water to a sump pit.
What that means is that they will have to crack the concrete all around the interior perimeter and install a perforated drain in a bed of washed gravel, leading to the sump pump. This will get covered back up with concrete. I found a few pictures online of what this looks like:


I think we're going with a contractor in the $5500 range; we need to verify a few things yet, but it looks like his price includes building a whole new sump pit. Ours looks in rather sad shape; it's metal and 30+ years old. They'll patch a few minor cracks on the walls as well. The estimator is going to check with his boss, but may be able to include putting a concrete slab in our crawlspace as well for the same price. We'll see. (The crawlspace is currently gravel, and never gets used. Having it available for additional storage might be nice.) Their lifetime guarantee actually is for the lifetime of the house (others guaranteed the work for 10 years) and is transferable to subsequent owners. Best of all, they can schedule it this week and get it done in a day because they have a large crew. Other estimates said it would take 2-3 days and we'd have to wait 2-3 weeks.
So, while a nasty unexpected expense, we're looking at a guaranteed dry basement as a good selling point in the future, adding value to the house.
So, now we have to tell our tenants, who just set up a jumbo aquarium in the unfinished basement, that they'll have to move it so work can get done.
Update: The contractor who was already our number one pick ended up giving us a new bid of $5000, which does include laying a slab in the crawlspace. Times are tough out there, I guess, and he knew we had other contractors making bids. It's definitely a good idea to comparison shop; even the well-rated guys (per Angie's List) are willing to make deals now. They're coming in Monday at 7:30 and should be done by 5:00. Can't beat that.