Quick Question : Does the Printer Alpha ROM module for the 9810 have to go in slot 3?
I've just obtained said ROM, and if it's put in slot 2, it prints blanks rather than characters (i.e. a program listing has a gap in the line of dashes where the function name should go). If it's put in slot 3, it's fine.
And I get the same results using 2 different 9810s. So, do I have an obscrue fault in both machines?

Yes, it has to be in slot 3. There's a big warning box in the manual saying this.

Thanks for the information. OK, I don't have a hardware fault to trace.
Incidentally, it's unlikely that plugging a ROM module into the wrong slot will do any hardware damage. The slots are all equivalent electrically, they just have different chip select lines connected to them, so the cartridge in the slot appears at a different address depending on which slot it's in. A bit more detail for those who are interested. The HP9810 cartridges contain 2 or 4 HP ROM chips. Each ROM is 512 bytes. They are wired up so the cartridge is either 512 16-bit words or 1024 words. There's a separate chip select pin for each pair of ROMs, there is no address decoding in the cartridge (unlike, say, the 9825).
The 09810-66523 (Red/Orange handles in the memory cage) handles memory addressing. One of the functions of this board is to provide chip select lines for 16 memory devices. Namely : 4 sets of ROMs on the system firmware board (09810-66521, red/brown handles in the memory cage), 6 sets of cartridge ROMs (2 sets on each of 3 slots) and 6 banks of DRAM (either 8 bits wide for dta stroage or 3 bits wide for program storage).
A different 2 outputs of the decoder are connected to each slot. This would explain why some (all?)_ cartridges only work in particular slots -- they need to be at the right address.