The crux of the 'problem' with regards to the secret identity is that:
We're in on it.
We see 'everything'; the characters don't.
As others have posted, there are numerous stories where Clark and Superman have been seen together in the same place and at the same time. There are photographs and video footage of them together.
Heck, there was even a 'time' when someone theorised that Superman and Batman were the same person...
The other misconception is that the DP-staff spend a lot of time with and around Clark. They don't. More often than not, Clark probably isn't at his desk - neither would Jimmy, Lois, etc be, either. At most, they probably have two hours of face-time over an entire day.