I've been playing the dump quite a bit and caught two more seemingly random glitches on this play session. The first one was after completing the fourth stage (rivets), when the game was resetting back around to the first stage (girders). When the screen went black after the ending intermission a teal colored "3" was shown all on its own in the upper right. Turns out it was my extra lives counter as the stage built around it and it turned the proper white color.
The other glitch came up on my second game, after looping the game three times up until the fourth cement factory stage in my previous game. Upon starting to climb the last ladder the entire screen flickered and the following graphical glitches were displayed...
The level continued to operate properly and upon completion and loading of the next stage the glitched tiles went away.
I don't know if these problems would come up on actual NES hardware but it wouldn't surprise me. Those looking to order a copy of this on a cartridge may want to tread lightly and be aware of the possible glitches.