While we have different opinions on it, I think most of us would agree the "need" list is pretty short, looking at the positions one by one, and taking out opinions as to if the player at the position is really good or really bad (which for some I know is impossible). I'm defining "need" as either no depth or there wouldn't be anybody to play the spot if the starter goes down.
Offense
Quarterback: No, 25 year old, healthy, has won a playoff game and two division titles. (Ages of players approximated)
Running back: No, 25 year old, healthy, two time rushing champion
Fullback: No, not really used much, not a highly important position.
LT: Yes, Smith wearing down, has had injury problems, not really a good backup available.
LG: No, Williams young, should get better as he gets stronger (if he can, assuming so) and used to playing guard instead of tackle. Redmond available, and if Frederick is back, Loone can fill in there.
C: No, assuming Frederick is back, which indications he will be. Looney capable backup.
RG: No, perennial All Pro.
RT: No, though it's close to being a need. Collins is serviceable, "good enuf"
WR: Yes, Cooper, Gallup and Beasley are the established guys, and that core is looking good. But Beasley may leave, Hurns has to recover from a severe injury, Brown and Lenoir haven't shown a lot. Need is for another no. 1 receiver, Cooper gets hurt and the Cowboys are hurting there.
TE: Yes. Jarwin and Schultz are young, have shown promise. But with the Cowboys using the running game for their offensive focus, and Swaim injured, need depth.
Defense
(Grouping the DE's, as they can and have swapped sides)
DE. No, Lawerence, Charlton, Armstrong, Jones. 4 is enough, plus Crawford, if needed.
DT: Yes. Though the Cowboys have plenty bodies, all are middle of the pack, skill-wise, need at least one much better player there.
LB: Yes. Smith and Vanderesch are young and have ability. But the rest are so-so, Lee unreliable, health-wise. Need another strong starter.
S: No. They have 4, none top notch but all serviceable. Again, talking need, not "we'd like to be better"
CB: No. 4 available, most young, really coaching is more a need than players here, and Richard is now here for off-season and camp teaching. Might get Earl, which would be nice but don't see it as a necessity.
P: No. Jones highly underrated, imo, even if not, he's plenty good enough.
K: No. Record long fg, by 6 yards. Good enough, hopefully the offense can punch in more tds in the red zone, not have to rely on long fgs.
LS: No. Laduceour (sic) is great. Assuming he'll be resigned.
So that's 5 needs, tough to get with no first round pick especially to get a no. 1 receiver, but should be able to at least get somebody to compete there....