With respect to Mickey Mouse specifically, the only reason anyone cares about Mickey Mouse is because he is associated with Walt Disney Co. He's more like an animated logo.
There is a separate section of law designed to protect such brand associations called "trademark". As long as Mickey Mouse is a registered trademark (which he is), TWDC will retain the ability to stop uses of the mark that would be deceptive or misleading.
Trademark protections are much weaker than copyright protections and apply only to commerce within the pre-defined areas in which the trademark is registered. Disney would lose the ability to lock up anyone who published an image of Mickey Mouse that they didn't like, but would still be able to protect its brand, as long as the public associated Mickey Mouse with TWDC in the relevant areas of commerce. This should be more than sufficient to stop, e.g., Universal Studios from putting up Mickey Mouse banners at their competing theme parks, implying an endorsement or association with Disney.
What it may not stop is a use of Mickey Mouse that doesn't imply association with or endorsement by the trademark's owner. For example, under copyright law, Universal cannot create a "Punch Mickey" attraction. However, one may be able to argue that such an attraction is legal when Mickey is only protected by trademark law, because then the only uses that are barred are those that are likely to confuse or mislead the consumer. I'm sure this would be litigated out if it actually happened and some judges are definitely stodgy enough to say that any use of someone else's trademark automatically rises to the level of misleading consumers (and we should not discount the rarely-discussed incentive that judges have to rule in favor of powerful interests, nor should we pretend that we don't see that on a regular basis), but under copyright there is no real way to argue that this is non-infringing.
The main point being that Disney would no longer be able to use the FBI as Rent-A-Cops to stop any use or depiction of Mickey Mouse that they disliked, under the auspices of "promoting the progress of science and useful arts". People who wanted to make their own unofficial Mickey Mouse content or merchandise would be free to do so without threat of arrest or lawsuit, so long as they did so in a manner that was not misleading about the association with Disney.
