ISP:
Time Warner Cable.

Type of Internet Connection:
Cable.

Internet Connection Speed:
15mbps download; 2mbps upload.

Date & Time:
The first occurring time I don't remember, as my game crashed right afterwards and I thought it was the game crashing.
The second time just happened now; 12:30AM EST.

Frequency:
Twice now; so sometimes.

Character Name:
Haruko Haruhara

Race:
Race of your character when the issue occurred.
Female Miqo'te

World:
Hyperion

Class/Level:
BRD; 50.

Area and Coordinates:
Leviathan Extreme; x:6 y:6

Party or Solo:
Party; 8 members.

NPC Name:
None.

Monster Name:
Leviathan Extreme; another instance in which I can't currently remember.

In-Game Time:
N/A

Steps:
-Load into an instance.
-WHM casts protect & stoneskin; there is no longer any animation for these buffs or anything else for the matter-- (this is just how I fist noticed the bug). Animations are ENABLED in my settings.
-Target anything-- a player, an enemy-- and there is no animation (no arrow, no ring at the bottom of your target) for targeting.
-Restart game client and everything is fine.