Jon's got an Army
The answer is simple. Because Jon has an Army. No one can arrest or execute him unless they deal with his Army first.
The deserters are usually taken by hunting parties of the Watch or in case the deserter makes it beyond Brandon's new gift, he is taken by patrols of the local lords. They are usually alone or in very small groups so they do not pose much danger to a lord who might be prepared to carry out the sentence.
Jon's different because he is the only crow (ex-crow) come down from the Wall with an Army. He had 2,000 wildlings at his back. The figure is even more impressive when you consider that for Second Battle of Winterfell, Warden of the North Ramsay Bolton managed to gather only 6000 men. Granted 6000 can easily cut their way through the meagre 2000 wildlings but that would require a full battle to capture the bastard of Winterfell. So in a way, Jon had about 1/3 power Warden of North could muster and thus it was sufficient to give any lord with that idea a pause.
Even Lord Bolton was forced to reconsider this factor and he had to make this offer to Jon in S06E09:
Now, dismount and kneel before me, surrender your army and proclaim me
the true Lord of Winterfell and Warden of the North. I will pardon
you for deserting the Night's Watch.
I do not doubt that had Jon surrendered his Army, he would have been slaughtered but he did not surrender his Army. Thus he could not be taken. Say what you will about Ramsay, but at least he remembered that Jon is a deserter, unlike other lords.
Lack of Warrants from Castle Black (Books)
From a previous answer, you can see the assertion on how Castle Black sends warrants for deserters (from books POV) and how do Lords distinguish deserters in their lands. In Jon's case, no such warrants were issued. And he made no efforts to hide himself.
Trust a bastard? Nopes
As for trust, People of Westeros generally do not consider Bastards to be trust worthy, even if it is Eddard Stark's bastard. We have most of evidence in this regard from the books, not the show.
Resurrection is normal? No
Coming back from the dead would be just as shocking as it would be in our world. The only resurrection that we have seen is that of Beric Dondarrion. And he is a fugitive lord-turned-outlaw, currently cut from rest of the world in Riverlands. Sure peasants may have come to believe he can't be killed but since they believe a lot of things, no one is going to believe that. From the Books we know that Beric's resurrection is considered to be failure of the men who claim to kill him i.e. they think that the claimants lied and they had never killed Dondarrion in the first place. Most of the realm probably hasn't heard of a Lord Dondarrion from Dornish marches since beginning of the War of the Five Kings.
So no it is not common in Westeros for a dead man to come back alive (Well at least without blue eyes shining like stars).
The Sansa effect
He also has Sansa. If they win (which they did), Sansa becomes Lady of Winterfell and Warden of the North (Even though in the books, it is a title granted & renewed by the Crown, in the show it appears to be a hereditary title). If Sansa confirms the story, Lords and peasants will believe it as well, well at least on the outside even if they harbor doubts. The Night's Watch under Edd Tollett might also confirm the event and make entries into their records. (Besides Edd is not the Lord Commander. He may be acting lord commander for now but what happens if brothers of Night's Watch elect someone else for their Lord Commander at election?)
The technical debate on termination of Service with NW
But it must be noted Edd does not agree with Jon's point that death is end of his duty. From S06E04:
Edd: How can you leave us now?
Jon: I did everything I could. You know that.
Edd: You swore a vow.
Jon: Aye, I pledged my life to the Night's Watch. I gave my life.
Edd: For all nights to come.
Jon: They killed me, Edd! My own brothers. You want me to stay here
The Vow contains two important parts indicating the end of service:
Night gathers, and now my watch begins. It shall not end until my
death. I shall take no wife, hold no lands, father no children. I
shall wear no crowns and win no glory. I shall live and die at my
post. I am the sword in the darkness. I am the watcher on the walls. I
am the shield that guards the realms of men. I pledge my life and
honor to the Night's Watch, for this night and all the nights to
Jon is sticking to the phrase that says that his Watch ended with his death. Edd is more of the idea that his Watch does not end because it is for all the nights to come. The pioneers of Night's Watch did not consider case of a bloke who gets resurrected when they were writing their vows.
In conclusion, it's Jon's Army which gives the lords of the realm a pause. If he loses his Army, pretty sure everyone will suddenly recall he is a deserter.
Personally I believe this is a serious flaw in writing. Not one house in North objected or asked about Jon's "desertion" from the Night's Watch when by rights they should have done so. We can make observations on why he was not executed, but we cannot make observations on for what splendid reason no Northern Lord was remotely interested in calling Jon a deserter and a traitor.