I ran a T20 campaign weekly for over 2 years, so some advice.
If you have the Traveller's Guidebook for Player's, you can ditch the D&D rules. (In fact I recommend it, not because they don't have the same rules but because it will help to get the player's heads out of D&D mode.) Also note that T20 was written with the 3.0 not the 3.5 rules as a base. (And there is a difference.)
Most broken? Gunnery Skill doesn't make much sense for lots of reasons, if you drop it and use BAB for gunnery as well as other combat. it helps. (Naval gunners take the martial feat to make up for the lack of BAB and things work pretty well. Large ship combat is too nasty, especially with the Gunnery skill in place (Spinal Meson + PMOS + Average Gunnery = Automatic Critical Hit and total destruction of any ship under 800,000 tons, and reducing SI to <0 of any ship over 800,000 tons but under 7.5 million tons.), but at least typical RPG level starship combat is in good shape.
Also note that Fighter craft are not Single operator craft (But since they all have a bridge (required) and therefore at least 2 seats, not a big deal.) due to the combat rules all ships require a Pilot and Gunner to be effective in Space Combat (Minimum, 4 plus one gunner per battery is better.). You can fly it or shoot it, but not both with only one crew member. Also note that the light fighter in the THB has space for a crew of 3.
Unlike LBB5, 2 equal fighters can engage in combat and damage each other.
For Players:
Most important Attributes are Intelligence and Dex (in that order), everything else is secondary regardless of class.
Characters MUST Specialize. It is tempting, especially if you are coming from CT to spread things around and multi-class all over the place. This produces characters that are poor at everything and less than satisfying to play. Players that followed the advice of specializing and placing Int and Dex as 1, 2 had a much better playing experience.
About 5 terms in Prior History is normal. More than that quickly hits the point of diminishing returns.
Weapon combat is exceptionally deadly and the system produces the desired results in most cases. Coming from D&D players won't realize that, Traveller Players always knew this. It may be best to have everyone create throw away characters, or let them play some characters that you create and introduce them to fire combat before starting to play with their actual characters.
Unarmed combat, on the other hand, is exceptionally long and boring with a typical group of characters trying to beat each other senseless taking most of a playing session and no results.
Note that in Vehicle combat, at higher tech levels, armor is better than weapons so high tech armored vehicles are notoriously difficult to damage unless they are getting fired on by starships.
Overall, with this in mind, the system is definitely playable. It has a CT feel using the D20 rules and aside from the gunnery skill the only house rules I used was my typical Cost is per parsec not per jump for travel and cargo house rule.