Leveling the pet with you, actually meant you leveling before it then it catching up, hitting 60 you were not done yet cus your pet was 59 still! Taming a new pet meant a good while of it playing catch-up.
Training abilities,.. yes training all those new abilities for yourself and having to relearn abils just stronger and better, then turning to that random guy next to hunter trainer who went by the associated "pet trainer" and then having him train your pet in new abilities!
Happiness Meter and Friendship Status.... having to keep a stock of food and in some cases specific food just to keep your pet plump and happy, having that green box face saying that your pet is doing 125% dmg and is feeling good! Always worrying about keeping your pet away from the red face, as you might lose a friendship rank! Doing just about everything to keep your pet alive so it stays happy, and then getting TO'd by any noob who went for the kill on your pet in a duel. I don't think I have EVER lost a pet due to happiness loss, but I sure know we ALL worried about that!
Good old Vanilla days,.. these things may have sucked but somehow I miss them...
And btw, how many of you still have that pet from those days? And if so was it a special tame? What was the pet? For me it was Rak'shiri, who I obviously named Rakshiri, and have relied on him on my original hunter and every hunter alt and this one ever since!