Don't forget to buff people when you get into a group.
Every time you die, make sure you check your buffs when you res. Everyone has a class buff and Sprint that will need to be reapplied; some classes have more (for example, a Jedi Guardian's Guard).
Keep your medpacks up to date - they heal for around 40% of my max health as a tank stacking endurance to high heaven. Same thing with stims.
If you've got the cash, orange (moddable) gear is excellent. A piece modded with all level 32 blues will be as good as or better than a blue level 32 piece of that same slot. Pick up mods with commendations or by buying new pieces of orange gear from specialty vendors and taking out the mods. There is a very appreciable difference between three levels of gear, and most of us will go 8+ levels before we remember to check for upgrades.
For those who've played WoW, a quick rundown on orange gear: it's like gem sockets, except the base stats are 0 because your "gems" make up the entirety of the item's stats.
Each piece of moddable gear has a "critical" slot (armoring for armor pieces, hilt for lightsabers, barrel for blasters, etc). This piece not only provides bonus stats (+strength, +critical, etc), but because it determines the armor rating/weapon damage of the item in question.
Most moddable items also take a "mod" upgrade or an "enhancement" upgrade. You can't mix them - i.e. a mod only goes in a mod slot, a hilt only goes in a hilt slot, etc. Weapons will also take a color crystal. There's some cool colors out there beyond the normal blue/green/red/yellow, but you usually have to work for them.
Weapons, chest pieces, and leg pieces are the most important slots you have. Weapons get four upgrade slots and chest and leg pieces get three.
Some quests will let you choose between a blue item and three commendations as a reward. Unless the blue is a fairly big upgrade, go for the commendations.
Keeping your gear up to date means you can solo Heroic 2+ quests and maybe even Heroic 4+ quests.
Do your PvP dailies (gotten in the combat training portion of your fleet) - PvP gear is some of the best in the game at level 50, and the PvP itself is pretty rewarding (in terms of fun, experience, commendations, and valor). Space Battle dailies (which you get in your ship) also give a good amount of experience and credits.
If you're short on money, don't be afraid to drop a crew skill for Slicing. You can level slicing to 400 as soon as you get it, and while profiting off it is less than intuitive, there are guides to help you out.