The movie starts off quite well, rather quirky, with colourful and fun characters played occasionally brilliantly by an excellent cast (Caine, Cook, Newman, Dudley), and visually nice, obviously with a decent budget. However, the first half is the part of TWB that sets up the story. The problem arises when the story unfolds, in the second half. That's when the gags take a backseat to a multitude of plot-twists, which become so dominant that you almost forget you're watching a comedy.
The writers of TWB would appear to have been so concerned with keeping the story clever (and it is, up to the point when it becomes a muddled mess) that somewhere along the way they must have forgotten to keep the story funny as well. There are numerous surprise twists, too many, in fact. The writers were so twist-happy, so bogged down in keeping this comedy interesting – as opposed to funny – that the twists spiral out of control toward the end, culminating in a not-so-grand finale which is just simplistic slapstick action farce, with people chasing each other and bickering in a buffoonish way.
I have never understood this compulsion, this annoying tradition to nearly always end a comedy with a boring action sequence. What the hell is that all about? Hence why so many comedies start off well, sometimes work well in the middle also, but then degenerate into daft and dull chases and shoot-outs whose only purpose is to serve the (more-or-less irrelevant) story. The problem is, who CARES about the story's resolution. A comedy needs to be funny, not resolved. If you can do both, then all the power to you, but get your priorities straight.
To watch Caine in an excellent comedy, as opposed to a solid one like TWB, you can do much worse than try "Without A Clue", "Blame It On Rio", or "Dirty Rotten Scoundrels". As for Cook and Dudley, watch "Bedazzled", which came out just a year after TWB; it's superior to it and one of the best comedies of the 60s.
There are some original ideas, such as the inheritors in a testament not trying to kill their uncle/father/whoever but dedicating their lives to prolonging their life, as is the case with "poor little orphans" Cook and Moore taking care of Richardson's health. (This is not a spoiler, as this is established very early on.)