The two fakes both refer to him as 007; the real Blofeld always calls him "Mr Bond". In fact, throughout the series, Blofeld nearly always refers to him as "Bond" (or some variation thereof).
It can be inferred that film takes place before On Her Majesty's Secret Service. Bond starts off DAF still in Japan attempting to tie-up loose ends and multiple times is referred to as Bond having been on vacation (which refers to his double life in Japan). Blofeld survives but gets all his newfound hair burnt off leading to OHMSS where Blofeld devises a much smaller scale but sneakier plan than before (presumably because the events of You Only Live Twice and DAF have almost bankrupted his organization). After Tracy dies at the end of OHMSS then we get Live and Let Die, where Bond is stunned when he hears about Tracey again so soon and it remains a sore spot for Bond for the rest of the series. Then finally Blofeld (still with his broken neck from OHMSS) dies in For Your Eyes Only and SPECTRE is kaput.
In Thunderball, SPECTRE demanded their payment in the form of Diamonds. Something that on the face of it would be far harder to convert into liquid assets of any use than, say, simple Gold that could be melted down and very easily washed back into the economy. Perhaps however the attempted acquisition of the very specific quality and type of Diamonds in that movie was an early phase of the plan finally realized in this film?
It's noted the envelope Bond is handed is too thin to contain $50,000 in any denomination short of rare $1,000 bills (discontinued in 1946). But Bond, when explaining to Shady Tree why the diamonds were fake, notes he wouldn't burn up $50,000 in real currency, so the envelope could be filled with fifty counterfeit $1,000 bills.
Bond uses a voice changing machine to intercept Blofeld's order to Bert Saxby to kill Willard Whyte. But then Saxby still shows up to do the job, making one wonder how he found out about the order. Since Blofeld noticed something odd about Saxby's voice, he may have called Saxby back, Saxby said he hadn't called Blofeld and Blofeld figured out what was going on. This is helped by the fact that he also moves up his plans by a day and leaves for the oil rig as soon as he can.
Blofeld has suddenly become a comical villain despite being cold and menacing in the previous films. But perhaps this is because he has snapped due to his many great defeats; in both the books and the films, he takes a lot of pride in his work, and his ego has clearly been damaged by now. He acts insanely and impulsively throughout the film, such as dressing in drag and making two girls guard a very important prisoner who is easily rescued. It seems that now he is so far gone that he does a lot of what he does just for kicks, like The Joker.
We never get a definitive answer as to why Blofeld is suddenly making doubles of himself and having corrective surgery again. (The first time was presumably to turn from Donald Pleasence in You Only Live Twice to Telly Savalas in On Her Majesty's Secret Service.) The good thing is, there doesn't seem to be one sole reason. You can go with the obvious: once knowing that Bond survived his assassination at the end of OHMSS, and since his wife is dead, Blofeld probably realised that he had woken a sleeping dragon and that Bond would come after him, so he had surgery AND doubles made up to throw 007 off his scent while he re-established himself elsewhere. You can also go with another theory: because he has so many schemes and plans running concurrently across the globe, Blofeld realised he couldn't keep his eye on everything at one, and he probably isn't too trustworthy to let someone else oversee his plans, so having doubles made and sent to various locations will ensure that the plans would run as smoothly as if he had carried them out himself.
Due to a Deleted Scene one is left to assume that Plenty O'Toole quite possibly had to return home without her clothes.
The fake diamonds, retrieved from the corpse of the real Peter Franks via cremation, are revealed to be mostly glass. Wouldn't those have been burned up along with the body?
Glass is not flammable, though it can be melted, and some types can shatter when exposed to intense heat. However, other types of glass can withstand the temperature found in a modern crematory. That being said, they would likely be discolored, and diamonds and glass can be easily distinguished.
Since diamonds are simply a form of carbon, they are essentially flammable: They will convert to carbon dioxide gas when heated to about 1300 degrees. A crematory oven actually exceeds that temperature, so burning a body containing diamonds might destroy them. Or perhaps our criminals didn't know that.
Why bother with Bond trying to switch the tapes when a guided-missile cruiser could have instantly destroyed Blofeld, the control tape and the transmission tower before he got a signal off? It's not like his last plot where he had "Angels of Death" scattered all over the world—here he's got all his assets in the one Supervillain Lair. And Tiffany isn't much of a hostage, given that she's ostensibly a criminal associate of Blofeld.