Translation:My uncle watches three Spanish channels.
You usually don't see something on tv, you watch something (systematically, in this case). I guess that's why it's not accepted. ^.^ You could use see in other cases, like
I saw it on the news. - Το είδα στις ειδήσεις. (Saw it at a certain moment, not actually watched it.)
He might also see three Spanish channels in the TV guide list. :) Relatedly, is κοιτάζει always wrong in this context?
Indeed. Well, this sentence is a bit too general for my taste. We might meed to change it up a bit, so that learners don't get confused. So I guess the only thing I can say for certain is in my previous comment, the tv-related usage of the verb. ^.^
If my memory is correct, in previous sentences the translation of the word "watch" ιn connection with television as "βλέπω" was rejected, the correct word being παρακολουθώ?
The word παρακολουθώ is correct, in this case, but in greek it's rare to hear somebody saying "Παρακολουθώ τηλεόραση", we say, almost always, "Βλέπω τηλεόραση"
this may be confusing, but it's also interesting. We automatically know that he isn't watching three channels at once, so it's a "present continuous" showing habit of watching. But if you're learning to speak Greek you don't need to know that, you just need to know "βλεπει" and "ειδα". Context will tell.