That opening monologue is a good chance to catch Benny's underlying charm, that is, when he slips gently into his reluctant-egotist act as the best comedian around. With most other comedians, that schtick could easily become obnoxious. But with Jack's basic likability, it's not only humorous but also oddly endearing. Same thing with his notorious "tightwad" act. We can laugh at these negative character qualities because we sense the man underneath is a genuinely nice person. Frankly, I don't get that same sense from many other comedians.
To me, the Bogart skit is a disappointment. It's neither well written nor does Bogart appear to be in the proper mood-- as other reviewers also point out. At the same time, the "voice-over" during the curtain call appears appears both odd and strained. For a guest appearance, it's an unusual few minutes and I wouldn't be surprised if there were an interesting inside story behind it.