In "The Metamorphosis," what are some changes in Gregor's father's charaterisics/personality?
This is a very interesting question, as you will find if you read the story carefully that the metamorphosis of Gregor actually triggers other transformations in his family, including his father. Note how at first he is described as a failure who is dependent on his son's income. When Gregor reveals his transformed self, he shows his weakness and also his anger towards Gregor:
The father clenched his fist, glaring at Gregor as if trying to shove him back into his room, then peered unsteadily around the parlour before covering his eyes with his hands and weeping so hard that his powerful chest began to quake.
Although he shows weakness, what stands out in his relations with Gregor is his anger. Notice how when Gregor attempts to leave his room, it is his father who violently forces him back, hurting Gregor both times.
It is the fierceness that dominates, however. The first two times Gregor ventures out of his room, his father forces him back in, the first time brandishing a walking stick and a newspaper at him, the second time bombarding him with apples. He does injury to Gregor both times.
Yet what is key to realise is how Gregor's tranformation galvanises his father, turning him from a "failed businessman" into the head of the family who starts dealing with their financial affairs with skill:
From time to time, he rose from the table to fetch some document or notebook from his small strongbox, which he had salvaged after the collapse of his business five years earlier.
Interestingly, though, he still shows elements of his weakness by the way he craves pardon from the lodgers. It is only when Gregor has actually died that he conquers his inner weakness, dismissing both the charwoman and the three tenants, who suddenly see in Mr. Samsa a new strength:
"Well, then we'll go," he said, looking up at Mr. Samsa as if, in a sudden burst of humility, he were requesting sanction even for this decision. Mr. Samsa, with bulding eyes, merely vouchsafed him a few brief nods.
It is key to note that Mr. Samsa is only referred to as such after his son's death. It is as if Gregor's demise gives him the release necessary to become the new man he has always shown the potential of being. Yet Kafka's text asks us a very hard question of why it takes his son's death to transform his father.