If you suspect line-noise, plug a noisy device into the socket next to the suspect clock and turn it on/off rapidly for a few minutes to see if the clock gains time. If your clock is susceptible to line-noise, it will gain time. I found that my Weller WTCPN soldering station is REALLY noisy; far more noise than my circular saw or garage vac.
My first-generation nixie-tube clocks use the 60Hz line signal for keeping time. I have 2 stages of low-pass filtering. The first-stage is for high-frequency/high-energy noise on the AC line, right where the AC line comes onto the PC board. The second-stage is a simple RC filter for the 60Hz reference signal to the CMOS counters with a cutoff frequency around 300Hz. Incidentally, my clock uses 4000-series CMOS gates, running at 10VDC. It has no transformer, and the "ground" of the clock is tied directly to the AC line. Yes, it's perfectly safe to run a CMOS gate tied directly to the AC line; no worries of surges, ESD, noise, etc because the other side of the AC line is well-protected and filtered.