When Stewie beats up Brian the second time, the beating started Stewie was hitting golf balls. To the left, there's a wall left from Stewie hitting the golf balls. But in the next few seconds, Brian puts on a disguise and walks right past Stewie saying "mornin'" without being blocked off from the wall when Stewie realizes that was Brian and Stewie chases Brian and they run right through where the wall should've been.
As Brian was sneaking past Stewie to avoid being beaten, he walks past the staircase before being discovered. Stewie then chases Brian in the same direction he was walking and the stairs reappear there for Stewie to push Brian down them.
When Brian is laying on the ground and Stewie is beating him up with the golf club, Stewie hits Brian's left leg, but Brian clutches his right leg.
Brian coughs up blood after he is hit by the golf club on his leg, and it isn't shown falling to the floor. It disappears in midair.