There was a period of time in which halting the landings on Omaha was considered, but soon after that moment of consideration there was progress made on the beach. So while there were a large number of casualties at Omaha but the defenses were still overcome in a matter of hours.

Was not doing so ever considered a mistake?

Not that I know of. The need to land at Omaha--which was recognized as a tough nut to crack long before the first landing craft hit the beach--was real. If the landings had not gone forward (and the enemy always gets a vote in combat) there would have been a fairly large gap between the British-Canadian force on the Allied left (Gold beach and the British to be specific) and the Americans on the Allied right (Utah beach to be specific). Without the force coming inland at Omaha, you have to find a way to keep the Germans out of that gap and fill it yourself--stretching hard-pressed troops to do more than they were already struggling to do. Allied command knew Omaha would be difficult, but it was still assaulted because not attacking it was even more difficult than attacking it.

Does all of that make sense? Followup questions from OP and others are always encouraged.