1. I'll see the dentist on Friday morning at 10 o'clock.
I'm seeing the dentist on Friday morning at 10 o'clock. (нужно употребить Present Continuous в значении будущего, т.к. речь идет о запланированном приеме у врача)
2. Our cat has been missed since five days. - неправильный выбор формы причастия и неверный предлог
Our cat has been missing for five days.
3. At last! I've been finding my contact lens. - неверная форма глагола. Нужно использовать Present Perfect:
At last! I've found my contact lens.
4. As soon as I opened the front door it was obvious that the house was burgled.
As soon as I opened the front door it was obvious that the house had been burgled. - требуется Past Perfect для указания на то, что дом ограбили раньше, чем это было обнаружено.
5. I hadn't got on very well with my father when I was young, but I do now.
I didn't get on very well with my father when I was young, but I do now. (Используем Past Simple, ведь действия в обеих частях протекали одновременно)
6. I hadn't worked for very long when I was interrupted. - в принципе, так можно сказать. Но раз надо исправить, то вот каким образом:
I hadn't been working for very long when I was interrupted.
7. Who's smoked? Can't you read? There's a 'No Smoking' sign in here.
Who's been smoking? (Используем Present Perfect Continuous, потому что действие завершилось совсем недавно)
8. I'll be finishing this book by tonight.
I'll have finished this book by tonight. - требуется Future Perfect для действия, которое завершится к указанному моменту в будущем
9. He's written a novel for the past ten years.
He's been writing a novel for the past ten years. - действие все еще длится, потому используем Present Perfect Continuous
10. Don't come at 7.00. We'll have supper then.
Don't come at 7.00. We'll be having supper then. - используем Future Continuous для указания на процесс, который будет длиться в определенный момент в будущем