I have experienced a very slow clock here in Australia. I bought a telephone answering machine in the USA in 1993 and brought it back to Australia. It used the mains frequency for its clock, so it ran slow hare... 50 minutes ticked over every 60 minutes. Damn. I opened it up, reverse engineered the circuit, removed the mains input to the RTC chip and used a very nice 8 pin IC that used the 50 Hz mains as a phase locked loop for a 60 Hz oscillator. The IC was bought at Dick Smith Electronics before it became a toy store. The circuit worked a treat.
Funny, I had a similar answering machine, with 2 tapes, and the incoming mains was used to drive the clock. I just looked in the "box of bits" to find a crystal that would divide down to 60Hz, and used a small bit of veroboard and some TTL dividers to get a 60Hz clock for it. As it also had the unfortunate thing of not having a working power transformer ( somebody had plugged the 110v device into 220V and burnt out the transformer, but the answering machine survived because it has voltage regulators to provide all the rails, and the 7809 and 7805 were more robust than the transformer) i also made a small power supply for it, giving a 12V battery backed rail for it, as the internal backup battery had a really bad timekeeping ability, it lost around 10 minutes an hour in battery backup. It also had audible prompts, and remote access ability as well, though I never used the remote side, mainly due to lack of a manual as I bought it on auction cheap as is. IIRC the crystal was 4.33 Mhz or similar, basically a NTSC timing crystal, from some item or the other that provided a microprocessor clock. After a bit of fiddling with a trimmer on the crystal it kept reasonable time, at least a few minutes a month. Had a built in oven as well, seeing as it was sitting next to the main aluminium plate heatsink inside the answering machine.
No longer around, it eventually wore out the rubber belts of the tape mech, and I also rarely got phone calls on the POTS line, more using it then for dial up internet.