Sorry no solution here, but also having the same problem and bumping this issue up some. Working on SW2012 SP1 x64.
when I explode a block the insertion point goes away instantly. that view to the right looks more like you are in "edit block" mode, not an exploded block...
Bump. I've got one stuck on a drawing as well. 2012 SP5.
I have had the same problem using 2015 sp2.
Finally found a solution.
When the blue circle shows, selecting the entity, SW states that it is a point (I was unable to delete this entity).
I have found that this worked for me.
Using sketch, place a new point (must be point) next to blue circle.
Using mouse RHB select blue circle.
Pull down appears, select Replace Entities.
Replace Entities pull down appears.
In Selection area - Replace this entity should show text - Point??? (??? = numbers)
Lower down - With this one: - and blank blue box.
With mouse LHB select the new point.
Select OK (tick)
Blue circle should disappear, then delete new point.