I managed to reduce the blurring by simply turning the TV brightness down. The text became much more readable. 

The text translates roughly into this:

Exception: Bus error, process '', load = $0, last syscall = 28
FC:4256 Acc addr:0051B122 IR:4242 Next PC:0051B122 SR:2008: t-S--------xNzvc
D0-D3: 0006FC86 00000000 FFF60009 FFA7FFFF 00000780 00000010 FBE50002 0????????
A0-A7: 0051D95C 0006F0C0 0006F1AC 0006FODB 0000FF2F 005001EA 0006F150 0006?????

Stack Frame:
06F0BC-0000 0780
06F0C0-0051 7202 0000 0001 0006 F0EA 8083 8483

With a stable screen, it looks worthwhile correcting the video shift-register error. 

The shift register sockets look like this:

Blue are the correct connections on the chip pins, yellow are the wrong positions on the socket holes.

Therefore, for each LS166 chip:

• Isolate the blue pins by bending them out of the socket,
  or if they are soldered in then cut the legs off the board but leave pin stumps,
  and remove the pin material from the holes.

Connect:

• Hole 2 to pin 14
• Hole 3 to pin 12
• Hole 4 to pin 11
• Hole 5 to pin 10
• Hole 14 to pin 2
• Hole 12 to pin 3
• Hole 11 to pin 4
• Hole 10 to pin 5

I didn't manage to isolate the pins neatly, so I removed them, cleaned the holes  and did this.

First add wires to the wrongly positioned signals:

Then deplete the erroneous pins from some turned-pin sockets, then fit them:

Then connect the wires to the right pins:

Yes, it looks messy but it takes less space than forthnutter's correction board.

With hindsight, it would have been easier to solder wires to the chips first, the poke them through the socket and PCB holes.

I must have got all the wires right, because I get a sign-on screen with the letters the right way round:

which immediately does at least two Exception screens before settling. This is a second:

I get the impression the system is less stable than before, when it would usually just throw one exception.