If the author is reading this here, I'd urge you to replace those RIFA metall-paper caps near the mains switch. At worst they're a fire hazard, at best they blow their nasty guts all over their general vicinity.

The 3478A is a pretty decent and versatile meter. It has three weak points though:

1. The aforementioned RIFA caps

2. A lot on the analog side is done by a hybrid, including driving relays, input switching and a bunch of trimmed reference resistors (current source gain and parts of the input divider iirc). Also, the mounting of the hybrid is also what holds the front/back input switch in place. Stuff's flexing a fair bit when using that switch! If that hybrid is shot, the whole thing is pretty dead.

3. The calibration is stored in a battery-backed SRAM on the outguard side of things. I don't think you can extract the SRAM contents, so battery swaps need to be done live. If you send one of these in for calibration, it's going to be about as expensive as another 3478A (n.b. the circuit allows you to do stupid things like e.g. shorting the battery for a short time, because the SRAM is fed by the battery and the power supply through or diodes, and there's a 1uF or something like that tantalum near the SRAM. I don't know how long it survives off of that cap)

4. Don't feed mains into it when in ohms mode.