How can you make Twilight Imperium games not take forever?
Some minor tweaks that can help:

1) Use the variant Imperial II from the expansion.  Tricky juggling of the turn order to ensure you get Imperial is one cause of delay in selection.  (Also, Imperial is badly designed and dull...)  That variant expects the goals to be face-up - which speeds the game up; everyone can see which vps they're aiming for later on.

2) Play to 1-2 fewer vps; that'll normally save a full turn, without damaging the endgame too badly.

3) Use a fixed board instead of dealing out; then the host can set up in advance and skip the board dealing phase. (FFG publish suggestions for this at the TI site.)

4) Assign admin tasks to players - make one player in charge of the planets deck, one in charge of action cards, etc.

5) Use a tech / status tracker or other ship reference sheet to keep quick track of tech effects on your units.

6) Get in the habit of planning your builds during other people's turn, or allow 'honor builds' in which you announce a build and then the next player moves on with the game while you build.  Builds need time-consuming decision making and are rarely affected by the next player's move.