Another hypothesis (not really an answer because I can't show a specific experiment):
The clocks were never 25 minutes slow - Doc's watch/clock on the other end of the phone line was 25 minutes fast.
(I like this hypothesis better than my previous one, but I guess I'll leave the other there just in case it helps someone else find a better explanation)
Supporting research for Doc's watch being 25 minutes fast
Doc said the clocks were "exactly 25 minutes slow", but we don't know what he was comparing them to. They could have been slow relative to a watch that he had been experimenting on. So, a more accurate statement may have been that the watch he was comparing the clocks to was 25 minutes fast (because it came from the future maybe?). But, Marty hangs up on him to rush off to school before Doc could have potentially explained that.
This theory is backed up by a later suggestion in the film that experiments have been done on Doc's watch(es) that make other clocks/watches appear to be running slow. Primarily when Marty first starts recording Doc before they put Einstein in the time machine. Doc time stamps the recording as 1:18 AM and Marty seems puzzled and thinks maybe his watch has stopped (which he awkwardly holds to his ear as if he could hear a digital watch tick). This suggests that Doc's watches are ahead of the time Marty expects them to be making Marty think his watch had stopped.
However, I don't think the time discrepancy observed by Marty at the mall is the same 25 minute discrepancy he observed at the beginning of the movie. In order for Doc's watch to have been 25 minutes ahead when it was reading 1:18 AM, Marty's watch (and presumably the mall sign) would have needed to read something along the lines of 12:53 AM. But, we know the mall sign said 1:16 before Marty started on his way to the van.
Marty didn't compare his watch to the mall sign that we saw though. So, at the point Marty was at the mall sign either:
1) Doc's previous experiment(s) affected the mall sign in addition to his stopwatches (allowing them all to potentially be 25 minutes ahead), but not Marty's watch - and Marty didn't notice (or at least wasn't shown noticing) the sign was 25 minutes off from his own watch
2) Marty's watch and the mall sign were both set to 1:16 (makes sense because Doc asked Marty to be there at 1:15) and Doc's watches were at 1:17-ish (stopwatches can't be 25 minutes ahead because they read 1:19 a couple of minutes later in the film)
While I do like the simplicity of there being only one previous experiment making a single 25 minute discrepancy (which fits with the one missing container of plutonium that @user46913 pointed out in his answer), option 2 sounds more likely to me than Doc's experiment affecting the mall sign. So, I like to think Marty's watch said 1:17 when Doc said his watch was 1:18. This is also somewhat solidified by Doc only sending Einstein one minute into the future (ie. maybe that's what he did in his most recent experiment with his watches also).
This doesn't allow for much time to pass between Marty being at the mall sign at 1:16 and filming Doc at 1:17, but this is Hollywood. They put 4+ minutes of film between the two clips of the stop watches that showed only 3 minutes had passed. So, I don't consider one minute of Marty/Doc's story being told using a little more than a minute of film to be too much of a stretch for the usual Hollywood time distortion.
And, I say Doc did experiments directly on his watch(es) rather than experiments on himself or Einstein that affected the watches because Doc does explicitly say that "Einstein has just become the worlds first time traveler" after he sends him a minute into the future. So, I doubt Doc sent himself or any other living thing worthy of the title "time traveler" before then. But, he left the possibility for experiments on other non-living things - ie just experimenting on clocks/watches.
Lack of evidence for clocks being 25 minutes slow
The only reference outside of Marty and Doc's conversation about the clocks in his workshop being slow was when Marty was explaining his reasons for being late to school to his girlfriend. But, this is questionable because Marty is apparently always late for school (late four times in a row according to his girlfriend and the school principal). Which means he could have been late even without clocks being slow. But, before his girlfriend could comment on his statement about Doc setting the clocks 25 minutes slow, the principal interrupted them. Perhaps she was about to say, "But Marty, you're only 2 minutes late." I guess we'll never know. :)
The only time pieces outside of Doc's workshop that could have backed up this explanation are the watch on Marty's wrist, and a clock outside a business when Marty is hanging off the jeep on the way to school. Unfortunately neither are in focus enough to see the time. You can almost see the time on the clock in town, but we don't know how long the ride was from Doc's workshop to the clock outside of the business anyway.