In the scene where the sisters first arrive at magic school Paige asks Piper and Phoebe how they got rid of the source before; when in fact she was there with them to vanquish the source the first time.
When Piper and Leo are sitting down at Wyatt's school play, the camera Leo is using changes from a larger to a smaller more compact one.
The Source immediately recognizes the Charmed ones even though their appearances are supposed to be completely different. As many other demons have done, The Source recognises the Charmed ones by sensing their powers, not their appearance.
Technically, Mandi (aka the possessor demon) shouldn't have been able to revive the Source. In the episode _"Charmed"(1998) {Witch Way Now (4.22)}_ Cole told Phoebe that the beast that inhabited the demonic wasteland had consumed the Source half of his personality and that put an end to him forever.
When the girls arrive at Magic School and see the resurrected Source, Paige asks how he was defeated the previous time. However, she was present each time the Source was vanquished.
Mandi resurrected "The Source", however the Source is not one particular demon, rather an essence that possesses demons and makes them the most powerful in the underworld (e.g. Cole Turner). She technically conjures the half-faced demon who was possessed by The Source right before Cole, but he lost the power of The Source when he was vanquished, and the power was lost forever once it was destroyed in the demonic wasteland. Basically, Mandi conjured a random demon who was once very powerful, but lost a considerable amount of power once The Source was transferred out of his being.