It would be quite annoying to have your clock off a minute every week. The first couple weeks wouldn't be too big of an issue, but when you start getting 10 minutes off you would need to fix your clock.
Nah, it'd be "trivial" (in the way that generates employment for programmers, win-win) for your cell phone and computer to adjust automatically. You might be able to just get the NTP servers to make the adjustment daily and everyone else would just follow along without knowing it. Fancier wall clocks, too.
If you've got a fancy watch, just go get its movement adjusted to run 10 seconds slow. Full employment for watchmakers too, it's a shovel-ready proposal!
Believe it or not but some of us still have dumb watches and clocks. I have a dumb clock in my bedroom, on my oven, and below my tv. I don't want to buy a fancy clock. I just want the clock to tell me the time and I don't want it connecting to my network just to be accurate.
And depending on what sort of dumb clock your dumb clock is, it probably has a screw somewhere to make it run a little faster or slower, or something similar, to tune the clock to make it run at the right speed. You just give it a slight adjustment and presto-chango, it runs at the new speed.
For clocks that take their timing from the frequency of the electric current in the power lines, that's fixable too.
It may be possible to change it, but its a hassle. I don't know if it is possible with something like an oven and wouldn't want to mess with something like that regardless. The solution to the time situation shouldn't be to be messing with electrical currents. That is just going to be a non-starter for so many people.