It has been 2 and a half months since the great time warp, and though 1.13.1 has been released we unfortunately did not see all of the world upgrade problems resolved. However, thanks to the wonderful larger Minecraft community, I believe it may be safe (enough) to upgrade using community-created patches.
There are some other relatively minor issues still, which I will do my best to describe below. Please bear in mind though that these are only the known issues (which I am personally aware of), there may be other rarer issues not covered here.
Nether fortress not spawning wither skeletons or blazes
https://bugs.mojang.com/browse/MC-133992
Nether fortresses generated in 1.12.2 or earlier may not be recognised as a fortress and continue to spawn blazes. The issue has been confirmed by multiple people, but the root cause of the issue does not appear to have been directly identified yet.
A similar report, https://bugs.mojang.com/browse/MC-125377, desribes other structures like Ocean Monuments not spawning structure-specific mobs within the structure after upgrading from 1.12.2 to 1.13 snapshots. This bug has been marked as resolved, but appears related.
Though this could cause some existing farms to be completely broken in 1.13+, it is potentially something which could be patched post-upgrade by inserting the data on the structure into the world files at a later date. However, I cannot make any guarantees.
Containers next to chunk borders can lose items when upgrading
https://bugs.mojang.com/browse/MC-134115
Double chests across chunk borders may have half their contents wiped. The root of this issue has been identified by the community and multiple different methods to fix this have been created. This issue is no longer a concern for us when updating to 1.13.1.
World upgrade is not proceeding correctly
https://bugs.mojang.com/browse/MC-136510
At a cursory glance appears to primarily affect non-vanilla-survival objects, the example given looks to be a spawner in a minecart which spawns Polar Bears (something not found in vanilla survival worlds without use of commands to create it). I do not expect this to affect our survival worlds, beyond edge cases where a Zedwick may have at some time created an unusual item for an event using commands.
Upgrading only unlocks oak button, pressure plate and trapdoor recipes and advancements
https://bugs.mojang.com/browse/MC-132442
1.13 has flattened many blocks from a single material (wooden_door) to many (oak_door, acacia_door, etc.). As the existing advancements and recipes covered all wood types with a single material, it is not possible to seperate them out and decide which the player would have truly unlocked during the upgrade process. So only the oak variant of the advancements and recipes are unlocked during the upgrade. The other variants can still be unlocked by the player after the upgrade.
TileTicks upgrader could cause update for unintended block
https://bugs.mojang.com/browse/MC-123692
Could cause blocks which did not have an update scheduled to update after the upgrade process. May under rare circumstances cause some complex redstone machines to temporarily break or mis-fire until manually reset.
I would like to know, given these issues and that the chest wiping bug fix has not come from Mojang, do you think it is time to update? Once we update, we will not downgrade again unless there are serious problems. I may not be able to patch small instances of data loss should they crop up, though I do not expect any to arise beyond the above listed structure mob spawning issue.