Multiple Gamemasters - First Transition

Last weekend we had a gamemasters session, which is a D&D 5e tabletop RPG where we take turns being the dungeon master in the same world. We've run this project for a few months now and last weekend we switched from the first dungeon master to our second.

Background
When we set up the group we all created 1st level characters and an adventuring guild to give us a reason to stick together. We decided that each gamemaster was free to run his own game and adventure. After a 2-4 session adventure we would switch dungeon master.

When we switched last week we actually first spent a few hours finishing the last adventure. Once that adventure was done we immediately started the new adventure with the new dungeonmaster. We decided that 250 days passed ingame between the previous adventure and the new one. The new dungeonmaster introduced the new adventure by inviting our characters to a wedding in another country. On our journey, we met another member of our order and decided to help him on his quest, which introduced the character of the gamemaster who was the dungeonmaster in our previous adventure. The transition was quick and flawless.

What was different
The first difference I noticed was the environment. We went from a temperate medieval kingdom to an arabian style desert environment.

A second difference was that the new quest was more personal while the previous adventure was tied to our adventuring guild.

A third difference was that the second dungeonmaster had a lot of puzzles and mind games, while the previous dungeonmaster was more focused on mystery and investigation.

A fourth difference was something I had dreaded, which was differences in rules. We had agreed to use the rules as described in the core rulebooks, but our first dungeonmaster often didn't have a proper grasp of the rules and thus made a few mistakes. Our second dungeonmaster didn't know the rules all that well either, so some of the rules were different from our first dungeonmaster and some rules were completely overseen. This may not usually be an issue, but I noticed that our bloodhound character is very broken already since he had created a character using one set of rules, levelled it up using another set, and is now running an adventure with a third set of rules. Hopefully this will get sorted as we play more.


What was the same 
I was afraid that each gamemaster would run the adventuring guild differently, but so far both gamemasters have run it the same way.

We're playing with the same characters, and they haven't changed. I may look into our bloodhound character when I'm the gamemaster to see if he needs to be fixed, but so far he's just as broken as he was in the previous adventure, which is a pity.

I missed the combat scenes in the last session, but I believe these were also very identical to our previous adventure.