In the video description it's mentioned that Cato's leg is warming up after only brief use, which definitely means you want to leave him off until you decide what action to take from here. The same thing was happening with Lizzy's back leg, caused by the motor inside trying to do its usual work of moving the leg with incorrect position sensing data, and you would at the least damage the motor eventually by continuing to run it like that. Which I'm sure you have heard from someone else already or suspected yourself.
It's interesting that the problem is intermittent, and makes me think that although your cousin's husband said everything was taped up and properly attached, there still may be a wire that appears properly soldered but has a failing join. Cato moving around would be disrupting that weak connection and your touching him would push things back into sufficient contact again so he appeared to work properly. The problem may not be immediately obvious to someone who hasn't worked on a Pleo before.
Replacing him is an option to consider, although there is the chance you could get a new Pleo who presents exactly the same problems. Lizzy is presumably from a much newer batch than Cato but has already had two leg repairs. Even though we obviously hear more on the forums about the Pleos with problems than the ones who work fine for years, I don't trust the quality of the from-factory wire joins at all. My boyfriend suggested that if you did decide to send Cato off to someone to be fixed that you get them to open up the other two legs that haven't had problems yet and make sure they're firmly soldered/glued in place like the one Kat has already repaired will be, so that you're unlikely to have more problems with them for the rest of his functioning life. Fixing legs isn't terribly invasive in terms of needing to cut your Pleo open so if you're experiencing wear and tear related problems now it might save you some angst later.
As to what you end up deciding to do, I guess it depends on how much more you feel able to invest in Cato, financially and emotionally. He is absolutely fixable as far as I can tell but it's difficult when you have to post him around to get him fixed. I'm sorry to see you finding yourself in this position.