When Max is reading the ransom note his cigarette is in his right hand as he drops the note. In the next scene it is in his left hand.
To raise the Chief's ransom, the CONTROL staff auctions off the contents of his office, raising a total of $600. Disposition of government property is controlled by federal law, and such an unauthorised auction would have resulted in prison sentences for Max, 99, and the others.
The Chief is frozen solid for his operation, and seems totally immobile. However, when Max and 99 are trying to "take him out," just before Harvey Satan comes back in (and Max says that "the prisoner was trying to escape,") we can see the Chief's feet moving quite freely, as though he is not frozen at all.
Max talks into his belt phone for several seconds without holding the mouthpiece in front of his mouth.