score:3
There are two unlikely but possible problems. First, if your total stay in Israel will exceed six months or whatever unusual shorter period you get on your initial entry, there may be an issue with the length. It sounds, however, as if Step One is a few days or weeks for tourism, in which case this is a non-issue. Second, the Allenby Bridge crossing is a pain in the neck compared to either the Jordan River Crossing or the Aqaba Crossing.
Many tourists do something like your itinerary, to include Petra or other Jordanian sites in a trip to Israel. Speaking of which, I recommend Petra very highly.