Personally, I think the biggest Omaha mistake is one made most often by players making the transition from Holdem to Omaha. In Holdem of course, a straight or flush is a very strong hand, if you are using both hole cards to make it. In Omaha the same is not always true.
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Although the hand rankings are exactly the same, and small straights and flushes still have some strength, comparitively your hand is very vulnerable in Omaha.
The problem with drawing to the smaller end of a straight or a small flush, is that all the opponents in the pot have four hole cards and this greatly increases the chances of you being up against a higher straight or flush. You have to be especially wary of this in Omaha hi/lo because of the value attached to hands such as (A,2,3,4), or indeed any hand containing an ace or two, and small cards.
In general terms, you should be attaching a lot less importance to hands which are not the best, or very close to the best hands available.
Other than this, I think the amateur players biggest mistake is not considering their pot odds before calling. You will often be in a position in Omaha when you are drawing to one or more strong hands. You need to be aware of exactly how many outs you have, and be careful not to consider cards that might make you a hand, but get you into trouble, as outs.
If you are looking to make a hand that would be the best possible out there, then you need to factor into your calculations the fact that you are likely to get callers if you make it, usually. Much more so than in Holdem anyway.
So don’t be afraid to be drawing to a hand in Omaha, but be careful not to call, trying to hit a draw that’s going to cost you all your chips.