Max isn't limping. At the end of the original film, Max ends up with a badly wounded knee - his wound is healed in the sequel, but he still cannot walk properly. Same thing in Beyond Thunderdome, where he still has problems walking. In Fury Road Max seems to be an absolutely healthy individual - at least when it comes to his physical health.
When it comes to his mental health - he has these flashbacks of his daughter - I've only seen the film once so I cannot be too sure, but it looked like a female child to me. In any case, a child, maybe 3-4 years old. In the original Mad Max his wife Jessie and son Sprog are killed - and his son was a toddler at the time who couldn't speak yet, whereas the flashback kid from Fury Road openly addresses Max - this could be attributed to his madness though.
In any case, that doesn't fit with what we're presented in Fury Road flashbacks - again, I believe a daughter is shown there, whereas Max originally had a son.
There is also a problem with the Interceptor - the original Interceptor was destroyed in the second film, and yet here it is again in the fourth. How many Interceptors does Max have?
There are also several other minor details which I don't find necessary to list at the time.
In short, George Miller made a fine film, but regardless of how much he tries to avoid the term - Fury Road is a reboot. It is definitely not a sequel nor a prequel, as it doesn't fit into any point in time between or after the previous three films.
Of course, it could just be a sort of retcon or an oversight (however, I refuse to believe that it is one), but in my opinion a reboot that is done in spirit of the original films is a much better alternative to a half-assed sequel that scraps much of the established "canon" (funnily enough, of all three original films, it contradicts Beyond Thunderdome the least, and we all know how "lore-friendly" that one is).
