What was that annoying behavior?
The usual, topped with a few X-specific WTF-moments.
First of all, the AI of the escorted ship decided to take the scenic route and bumbled merrily along paths that would or would not take it closer to its intended target. Second, it didn't bother to dodge but decided to take those shots directed at it like a man.
(These are common problems with escort missions, not limited to X specifically).
The X-icing on the cake was that you always escorted several slow-as-molasses, chronically underarmed/armored freighters, and that the enemies encountered depended on your combat rank. Which means that in the beginning, you had a few fighters to kill, while in the end, the game threw corvettes and heavy fighters at you in minute intervals, rendering the missions unplayable since the ships you escorted would explode if only hit by a few stray projectiles.
But yes, escort missions deserve their own thread, since they easily become the most avoided mission type due to errors in the implementation.