Should I be concerned about this roof?

[Whats the crack]

Any thoughts on the state of this roof? I’ve been told that the tiles should’ve been cut flush to the wall, there is some damp on the chimney breast in the house. But there’s no ventilation on it either.

 

I’m thinking it could be a quick fix of putting event on the chimney breast and having the tiles cut and levelled properly?

[Iceverge]

My fear is that a gale would send those tiles to the next parish but I suppose it's not as windy where you are. 

 

A vent in the fire would be a good start. Others any rain or damp that finds its way in will never dry out.