Plot hole: In season five, the show depicts the aftermath of an Electoral College tie. The procedure in this case should be the House holding subsequent ballots until a president is elected. On the show, however, Tom James convinces the Speaker of the House to hold one ballot, and then not vote again. James' plan is to win the Senate vote for VP, then act as president for four years before being elected to two full terms as actual president. James is outmaneuvered and his rival Montez is elected VP, and subsequently acts as president for the remainder of the series. After season 5, the show makes no mention of the House ever taking up a vote for president again, and the show simply treats Montez as the actual president. A Speaker of the House blocking the election of a new president would likely cause a political uprising from supports of both candidates, and both candidates would rightly take to the airwaves to demand a new vote. The idea of a power-hungry politician such as Selina, who uses every trick in the book to promote herself and elevate her own power, putting up no fight is just bizarre.
Plot hole: When Connie uses the wish machine to make Malloy small again, she instead wished for Ethel's breasts to get significantly bigger. However, in the next scene Ethel's breasts are back to her regular size. The plot shows that the wish doesn't wear off, and someone else would have needed to wish for Ethel's breast to get smaller but no one did.