The biggest proof that Walter is in town is that the stolen car from the cold opening was found in the town.
(Marie) That car they thought he stole in New Hampshire, they found it in a Denny's parking lot right on Central.
Since Walter was phoning his son at school and the DEA, the police was alarmed and they were searching for him, which is why the have found the stolen car so fast.
Beside the phone call from Carol to the police, we can only speculate who was doing the calls like Marie does (I would say it doesn't matter since by Walter phone call from New Hampshire and the stolen car in town, it's very sure that he is there for everyone. Beside that it's not clear if it is distraction from Walter):
(Marie) Skyler, we're getting calls from all over town. He's here, he's there, he's going to blow up city hall. [...]
(Skyler) Who's making these calls, him?
(Marie) There are two or three different voices. They're not sure if they're crank calls or people he's put up to it or if they're actual anonymous tips.
My personal guess would be that Walt has set up the calls in order to distract people and maybe he used Badger and Skinny Pete to do so.