I love that clip!
Two of my favorite George Martin statements concern that clip and song. First, George was talking about how the Beatles progressed as songwriters so quickly. He said that when they first started, "Love Me Do" was about the best that could do - but within a few months they just took off.
Second, he talked about the recording issues. The way the song was written and origianlly recorded, John sang the line "Love Me Do". John recorded the harmonica on a seperate track. They "tried out" the song live at some small venue, and before going on stage, realized that John couldn't sing the line and then come in with the harmonica. So, Paul was elected to sing it - just before going on. Paul was terrified. George thought that was funny, given what a great musican and vocalist Paul is.