Spelling..

When approval to an alliance is pending...
request is awaiting aproval

When you apply to an alliance, "application" is misspelled.
When you are accepted into an alliance, "congratulations" is misspelled.
When you are disbanding an alliance, "dissolve" is misspelled.

Deposit, not depozit (in the logs)

In the DDAY description, "stopped" and "set" are misspelled.

Under the announcements for credit exchange,
as long as it's done from whitin the game

Add-free is hyphenated, unless you are giving free ads.

After accepting a true request, "appear" is misspelled.

Under sending donation bonus, friends should be friend's (and in the announcements about it).

Insert a comma into "Be advised that the bigger the mothership gets the harder," between "gets" and "the."

In the nav computer, "coordinates" is misspelled.
When you add something to the nav computer, "through" is misspelled.

When you attack a person with no fleets, "opposition" is misspelled.

When you raid a person's base too much, "past," "automatically," and "approach" are misspelled. Also, there should be an "of" after "location."

In much of the galaxy views, "system" is misspelled on the window header as "sysyem".

In the commander window, "expertise" is misspelled.
When you change your avatar, "manually" is misspelled in the displayed message.

On the facilities screen, "warehouse" is misspelled once as "wharehouse."
In the following sentence, "a attack" should be "an attack."
The biofarms description doesn't have a period at the end of it.

If you try to take an action with reavers in the area, "out" is misspelled.

In the galaxy buildings list, "debris" is misspelled in "Advanced Debris Collector."
Under Sentient Engineering Matrix, "fleets" should have an apostrophe after it.
Under Nanites Assembly Facility, "resupply" is misspelled.
"Appetite" is misspelled in "Psychic Appetite Inductor."

In the default fleets, "inteplanetary" is misspelled, as are "barracuda" and "python."
In default special systems, "space distortion field" is misspelled.
In default weapons, "electron pulse ray" is misspelled.
"Stelar converter" means something different from what I believe is intended. "Stellar" was likely the spelling you were going for. It amused me when I looked up stelar, though.

Under personal truces, "truce-breaking fee" should include a hyphen.

In bounties, "decreated" is not a word. Was "decreed" the intended word?
"Calculations are ~~for~~ 10 million credits for 1 million fleet power." The first for is not necessary.
"Minimum" is misspelled in "minimum reward."
Not entirely sure, but I think "on-screen" should be hyphenated, written as "onto the screen."

I'm not entirely sure if "can not" is correct (I don't think it is, as it implies ability not to do something, rather than inability to do it), but I would change "can not" to "cannot" in the message that appears when a non-leader attempts to request a truce.
...Other people will have to check the things leaders can do, from truces to accepting, and so on.

In the place where you can upgrade to gold, "absorption" is misspelled in "search fleets by attack...absorbsion..."
"Necessary" is misspelled under the boxes indicating fleets and systems available.
"In-game" should be hyphenated, I believe.
"Its creator" should not have an apostrophe.
Other people with gold accounts should proof the gold-only things...if I get gold, it will be at the beginning of next round.

In missions, "losses" has two consecutive s's.

In the reavers encounter, "without" and "through" are misspelled, and the first two lines are missing a period. Actually, the first line wouldn't be a complete sentence, perhaps it is more of a subtitle. But the second one is definitely a sentence, with the exception of a missing period.
In the mothership encounter, "scavengers" and "launching" are misspelled.
In the bio encounter, "involving" is misspelled.
In the supernova encounter, "scavengers" is misspelled.
In the black hole encounter, "nowhere" is misspelled.
In the commander encounter, "according" and "through" are misspelled, and a "from" should be present after "ejected."
In the endangered planet encounter, "converter" is misspelled. Also, "people" is misspelled in the popup explanation.
When a commander fleet is present, "together" is misspelled in the popup explanation.
"Careful" is misspelled in one of the popup explanations, I believe it is the mothership.

When clicking on the picture of the mothership encounter (as you would to view an alliance description), "illuminating" and "within" are misspelled. Also, I would change "transcend" to "transcension."

I'll edit the rest of the ones I find into this post.

...I used to be incredibly good at spelling, and have gotten pretty good at grammar. Hopefully I won't miss much.