Ill try to write some of my suggestions here.
Technical
1. Main font. Its not defined

Browser will use default ugly times new roman. Maybe add some almost invisible gradient to default tables.
Here id screenshot, i added gradient in that cell market red, and changed font to arial.

2. "Remember me" misconcept. It should login user automatically, not remember password (actully hash of pass) in form - its browser functionality.
Another login issue. Usually sessions last until you close browser, unless its online bank. Its annoying to login every 30 (?) minutes of inactivity.
3. Maybe some AJAX in spaceo. It allow partial page loading, just as post preview button.
Lets imagine weapon designing. Instead of loading next page, after clicking view desing, weapon parameters pop below form. You dont have to hit back button to tweak more, just enter different values, and click...

*click* And system cost appears. There are lot of places where it could be used, in example in galaxy travel, instead of popup.

One thing to consider is AJAX libraries witch weight some kbytes, but they are downloaded once, and then save bandwith and server time all the time. Or make systems calculation completeley client side.
4. Allow dots in auction bids, stash etc. inputs (remove them on server side).
Gameplay
1. Encounters while traveling.
When a lot of ppl are doing galaxy encounters, if you have no luck, you might just waste turns for searching encounters, and get none.
Maybe add random generated encounter while performing jump to next planet in galaxy. It should be generated only for current player, and disspear if left behind.
I lost lot turns in previous round just to travel around empty galaxy.
- Prepare to jump
- Yes sir
- Speed 0.1c
- Speed 0.2c
...
- Whats that captain?
- Uhmm it looks like blackhole
- Should we abort jump?
[ Here player decides ]
- Yes, abort, we must check it
[ Player lost turns for jump, but can attack event ]
2. Well i dont remember
