The bug

There are a number of things whose movement isn't based on tick speed, instead moving in real time. This means that when there is large tick lag, some things will behave oddly. There are 2 different categories of these:

1. Most of these just appear to move too fast, but actually don't. They will render as though in their new position, but are actually where they should be. Some of them can appear glitchy, sometimes appearing to snap back to their true location or disappearing for a while. Others appear perfectly normal:

Glitchy:

Daylight cycle
Bottle O' Enchanting
Arrow
Thrown Potions
Snowball
Fireballs
Small Fireball
Firework rocket
Shulker bullet

Normal:

XP Orbs
FallingSand
Dropped items
Dynamic block textures
Dynamic entity skins
Particles

2. Then there are the ones that actually do move based on real time, therefore becoming out-of-sync with other game objects if there is a large amount of tick lag:

World border
Player movement and actions
Boat movement with player mounted
Horse movement with player mounted
Player placing/destroying blocks

Notably, minecarts with a player mounted work as they should, along with regular mob movement, status effect duration, and other things.

An easy way to induce tick lag with no frame lag is to summon a few entities and put "execute @e ~ ~ ~ testfor @e" on a clock. Be careful not to have too many, as too much lag can corrupt the world.