Prenotes: This bug is not due to lag!
It will happen if there is lag (client/server based) but it will occur either way

This bug concerns all projectiles, some more, some less.
I will list them and describe the symptoms:

Arrows:
This is only slightly noticeable and after the flew for a while
If you shoot them far away you can see that after ~2 seconds flight time they will sag/fall more than they would normaly do but just for one moment.
Look precisely and you will see that the arrow drops down for a bit

Snowballs:
Right after you shoot a snowball you can see the it will rise up.
Its like a stuttering and it will go up for a small distance, nothing the snowball would normally do they way you shoot it.
Also have a look at the gif file

Eggs: Same as snowballs

Ender Pearl: Same as snowballs

Eye of Ender:
They are also very stuttery and before they reach the top when they fly up, they will also make this "big rise" .
Another bug is that they are shot from the feet and not from the hand height

Throwable potions:
Kinda the same as snowballs. They are being slightly pushed up after you throw them

FireBall/FireCharge:
If you fire a fireball by a dispenser it will fly straight but right after you fire it, it stutters and then its accelerated very fast. So the "rise up" I mentioned before is in the horizontal direction.

This stuttering is not just annoying, you won't be able to hit over large distances as the accuracy is no longer stable.