Ben tends to play loose and free with how he wires things up.
You've left the data pins (26-33) of the 6502 floating, which means that it could be seeing just about anything when it's going through it's initial start sequence and reading the boot address. At the very least I'd tie those to ground, though later Ben will wire these to give the value of "EA" which is the instruction for "No Operation" on the 6502
It also appears that the BE (Bus Enable) pin 36 is also floating. Might want to make sure that's being pulled high. (A bit hard to tell with the blurriness of the picture if I'm seeing that one correctly or not though.)
Also, with the reset pin, you want to make sure that it's held low for at least two clock cycles.
On your 555 circuit, I'm not sure that's correct either. Looks like you have your POT going back to pin 4? Think that should be pin 7 (which looks like it isn't connected to anything).
Might double wiring check here:
https://www.allaboutcircuits.com/tools/ ... e-circuit/Edit:
You could also hook up the 555 as a debouncer and just use a push button to cycle the clock manually.
Edit Edit:
Looks like you have the exact same brand/make of breadboard power supply I started with. Keep a close eye on those and make sure they are in fact putting out 5V. All of the ones in the pack I got eventually died and started outputting wildly wrong voltages. (Fired at least one of my parts as a result.)