Sony already has things locked down through The Amazing Spider-Man 4 as well as two spin-off films (aka, Sinister Six and Venom), but potentially delaying the third installment might indicate that the studio is rethinking their strategy. It currently holds a release date of June 10, 2016.
The Amazing Spider-Man 2 opened this past May and was not only knocked out of the #1 spot after just one week, but it also recorded the lowest box office numbers of the entire franchise. Yes, that includes Sam Raimi's trilogy. The film is also expected to be surpassed by X-Men: Days of Future Past which would mark the first time in history that an X-Men film beat out Spider-Man.
The script for the third film is already completed, Marc Webb is set to return to the director's chair, and production was supposed to begin later this year. However, after the overwhelmingly negative reviews of TASM2 and underwhelming box office numbers we have not seen any signs pointing to a quick start for TASM3, thus making the rumored delay somewhat feasible.
Now... if this movie is delayed it will cause a ripple effect. With Sinister Six and Venom being pushed through rather quickly, it is possible that we might see the spin-offs before the third Spider-Man. It has already been said that Sony planned to cram Sinister Six in 2016 with TASM3 as a setup for TASM4 and Venom.
Seeing that the villains were one of the biggest complaints about TASM2 I won't be surprised if one or both of the spin-offs gets scrapped. Trying to revive a quickly dying franchise with an all villain installment might not be the best move at the current moment. Seriously, when people say the villains in Spider-Man 3 were better executed you know you have a major problem. With this it is also a possibility of TASM3 being limited to one villain instead of multiples.
Either way, I think we are bound to see some changes with this franchise. It's unfortunate seeing that The Amazing Spider-Man is only two years old.