Having a multi selection and at least one 'older' arc the startpoint indication in red of some entities might disappear.

Entities that suffer from this are:
Other arcs
Polyline
Splines

Only the 'oldest' arc in selection will have a startpoit indication.
Multi selection of 'newer' entities from the list above will not if an 'older' arc is part of the selection.
Deselecting de 'older' arcs will reveal the startpoints up to the 'oldest' arc.

In the file provided entities where drew in order from left to right.
Select all and start deseleting arcs from the left.

The behaviour is affected by changing the draw order property and a save/close/open.
In the second file the rightmost arc was set to draw order 7, the same as the 4th was.
After save/close/open it is renumbered to 8 and the behaviour is different as in the firts file.

Regards