When running command from Start > Run, the command exits before I can see the results

When I run certain commands from the Start Menu (Start > Run), the screen closes and exits before I can read the results. If, instead, I run the command in a Command Prompt, the display remains until I exit or clear it (normal behavior).

This is not a big issue since I rarely use the Start > Run field for anything. I am just curious to know if there is any way to hold the window open until I dismiss it?

For example, if I run chkdsk from Start > Run, I can see the various steps working but the window flashes away once finished - I'm unable to read the results. If I run chkdsk from within a Command Prompt, the results remain until I exit or clear the screen.

Yes, if you prefix the command with cmd /k in Start > Run, it will keep the Command Prompt open after execution has finished. For example:

cmd /k chkdsk