I do not doubt that this is true, but can anyone explain why we have not heard of such problems with lead acid or NiCad systems? There are scads of 24 volt systems of all battery types in aircraft, marine, and ground transportation equipment, all of them having 12 cells in series.
It's totally different chemistry. Lead-acid batteries have a nominal cell potential of 2V, so 12 of them will give 24V. The early ones with liquid acid in them are clearly a risk in aviation and even now, if you want to take such a battery on an aircraft (as part of a wheelchair, etc) you have to make arrangements to drain the acid and leave it behind, then get more at the destination. Newer dry-fit batteries with a gel rather than a liquid are OK. There's a potential explosion risk if you abuse the battery to the point at which it generates hydrogen. The energy density is relatively low, so they're not really good for aircraft because they'd be too heavy. For cars, they're good for powering the starter motor because they can provide the capacity relatively cheaply compared to other technologies and the weight is less of a issue.
NiCad and NiMH are fairly common, with the NiCad falling out of favour due to the cadmium and the fact that they perform less well than the metal hydride cells. They give about 1.2V/cell, so you'll need 20 of them to get 24V. This is what's been used in aircraft - better energy density than a lead-acid cell, but more expensive. The charging method is different, too. The cells are fairly robust.
Lithium cell technology is a lot more interesting. It is possible to get primary cells (i.e. not rechargeable) and secondary cells (which are). The contents are highly reactive and can catch fire or explode, especially when short-circuited. The common rechargeable cells give a nominal 3.7V/cell so your 24V is going to be either eight or nine cells in series. They're very picky about being charged, the temperature is important, below 0C or above 40C needs care and usually you just don't bother (typical for consumer gadgets such as phones). It's possible to charge at temperatures up to 50C at a lower capacity. If you apply too great a charge voltage (>4.2V/cell, lower at high temperature) then different chemical reactions start occurring and interesting things can happen. They also don't like working at all as you go over 60C. Unlike NiMH batteries, Li-Ion cells are endothermic on charge, so they will cool slightly. The other side of this is that they're exothermic on discharge, so as well as resistive heating, there's some chemical heating going on. If you're not careful you can get metal dendrites growing from one of the electrodes, puncturing the separator between the plates, and then shorting to the other one. This is not good, as it's a dead short across the battery and lots of heat gets generated which can melt things and make it worse, boil the electrolyte to increase the cell pressure and lead to the sort of catastrophic failure that has been seen. The energy density is better than other cells, which is why Boeing are trying to use them. Today I had chance to compare a 3.6AH NiMH battery and a 4.2AH Li-Ion battery of equivalent size and the Li-Ion was noticeably lighter with 16% more capacity.
inetdog has already touched on the difficulties of charging a string of cells in series regardless of chemistry type - inevitably one will reach full charge before the others so you have to deal with that, and it's usually done by attempting to match a group of cells to minimise the differences. Overcharging often results in capacity loss, so next time the problem will be even worse, in a spiral of doom down to cell failure after repeated charge/discharge cycles.
In a previous job I had dealings with lithium C-cell non-rechargeable batteries. They had to be shipped in boxes labelled "not to be transported on passenger aircraft", and the paperwork for DHL/Fedex/UPS to carry them is fairly dire.
Lithium is a really good battery technology until it goes wrong, at which point it gets quite scary.