Did Robb make the corrct choice when he condemned Rickard Karstarck?

He did the only thing he could have done. Karstark had committed treason and murder in flagrant defiance of his king, and to do anything else would have destroyed Robb’s standing among all of his other lords.

Moreover, and this is easily forgotten because of the quick sequence of events and differences between book and show, Karstark had already ordered his men to desert and hunt down Jaime by the time that Robb passed judgement on him. The damage was already done, Robb had already lost those men.