There are numerous bugs with the mounts that I have encountered with mounts and that my friends have encountered.
Griffin Movement Bug
When you use your griffin and mount and begin to fly you may find yourself unable to move your griffin. The mount may be inclined to move to the right or left and when you try to move him towards the direction you want it may go the opposite direction or just keep him straight. Also the griffin will have a camera view problem that will enable you to move the camera with your arrow keys but your griffin will not change direction.
Griffin Pocket Raptor Problem
When you fly above verdant brink at incredible heights nowhere near the ground, you can get killed by pocket raptors which are really far below you. They should no means be able to hit you, but sometimes they do hit you and kill you instantly causing you to fall far to the ground.
When you try to mount sometimes it does a number of bugs based on the mounts you try to hop onto.
Mount De-mounting Bug
When you demount using the X button when you are on a mount. Sometimes your character will show that you are still mounted on your abilities bar and you can't do anything unless you hit waypoint or 'sometimes' use your mouse cursor to hit the demount button.
Flying Raptor Bug
This is a recent bug that happened to one of my friends and is honestly quite hilarious. This player does not have a griffon and when they get on their raptor they can sometimes fly their raptor like a griffin. The raptor will be stuck in a static model position and the player can literally fly his raptor around the map. It looks hilarious and had the guild laughing for a good half-hour. Despite this the bug needs to be fixed.
MOB attachment Bug
When you are flying on a griffin sometimes a mob from the floor levels will get attached to your mount and try to attack it. I had the fun opportunity of having a Veteran Vinetooth in Auric Basin follow my mount and keep clipping to my position even though I was flying high above the map. Eventually the MOB will leave you alone as you leave the position it patrols, but it can be frustrating to have a mob hit you in the air as you are flying and you can't avoid it.
Honestly the most annoying bug on here is when you have the mount and you lose the ability to control it. I have done many parkouring events with my mounts only to lose control of my mount and have to wait for my mount to hit solid ground so I can demount and remount again so I can try to redo what I had done before. This is a frequent bug and is painful to deal with.
This bug is universal. All classes, races, and servers deal with this issue from what I have seen myself and heard from others. Every map build from HOT, Tyria, to POF experiences these issues.