How did Rin record the wrong channel in Episode 4?
If you pay attention to her dialogue, she mentions pressing a strange button. That did it.
She's Rin. It doesn't need figuring out. Magecraft genius yes, tech literate...no...
She also had Archer right behind her the whole time. Unless she changed the channel after kicking him through the roof, you'd think he'd notice it was the wrong channel. But then, maybe he let that one go to screw with Shirou.
AKA: Himself. Or it could be because he remembered it happen, but if he remembers it that means it happened which means he OH GOD MY BRAIN!
What are alternate timelines?
Isn't Archer basically just laughing at Rin's incompetence? He knows she's screwing it up, but she told him she could do it herself and refused his offer of help, so he's just letting her make a mess of it.
Basically, what happened was that Archer, after being denied, decided to let Rin suffer for a bit. After time was close to running out, he gave her the same advice... but she took a little while to listen to it and ended up recording another show.
Where did Ciel's tattoos go in the beach episode?
Ciel's "tattoos" have always been something like body paint, she takes a shower to remove them in Tsukihime right before an H scene. Ciel probably can't even get tattoos, due to her "condition".