Bear in mind when and where it was made!
I've seen some of the reviews of Fist Of Fury and some of them seem to be looking at it from a 21st-Century perspective.
When reviewing a film made in 1972 it's important to realise what was going on at the time. From what I've heard Chinese and Japanese really didn't get along all that well back then, and the movie was made for Eastern markets, not Western ones, so what seems a little OTT to us was a big deal to them back then. In order to see what an impact movies like Fist Of Fury had had on the 1972 cinemagoing public you need to see examples of other HK movies released around that time -- they contained hokey bits like flying swordsmen, perfect fighters and the so-called 'swingy arm, swingy leg' style of fight choreography -- some of which is in Fist Of Fury; basically any fight scene not containing Bruce Lee was not choreographed by him, hence the difference in feel)
Regarding some of the hokey bits, I expect a lot of that was director Lo Wei's 'experienced' input. It's no secret that Bruce Lee and Lo Wei didn't get along (no surprise the two never made more than two films together), and many say that Bruce would not have had scenes like the one where he goes up unarmed against a guy armed with a katana, or the one where he lifts a whole rickshaw, if he'd had any real say in the content -- something confirmed by the fact that there were no such ridiculous scenes in Way Of The Dragon and Enter The Dragon, where Bruce had far more control of the choreography.
Also, remember that Hong Kong budgets were shoestring in comparison to Hollywood movies (something which remains true to this day), so they could not afford to make things too flash. Even so, what they do achieve is still amazing considering the budgetary limitations.
Bruce could act anyway; in fact, he was a former child star in James Dean-like rebellious roles long before he became a martial arts action star. The reason some of the acting sounds OTT, particularly when people are angry, is mostly because Cantonese is a tonal language -- as well as pronouncing the word correctly the tones used also differentiate between words.