No way it was a red card, there was no intent, he was jumping for the ball with a leading arm, not swinging elbow. The ref did not even give a foul at first. Maybe you could make the argument that it was dangerous play, akin to foot-high, but no way was it a clear red.
This is what the laws of the game state:
(
http://www.thefa.com/TheFA/RulesandRegulations/~/media/Files/PDF/Get%20into%20Football/Referees/LOTG201011.ashx/LOTG201011.pdf)
Sending-off offences
A player, substitute or substituted player is sent off if he commits any of the
following seven offences:
• serious foul play
• violent conduct
• spitting at an opponent or any other person
• denying the opposing team a goal or an obvious goalscoring opportunity
by deliberately handling the ball (this does not apply to a goalkeeper within
his own penalty area)
• denying an obvious goalscoring opportunity to an opponent moving
towards the player’s goal by an offence punishable by a free kick or a
penalty kick
• using offensive, insulting or abusive language and/or gestures
• receiving a second caution in the same match
The only ones that potentially come into play are serious foul play or violent conduct. Gerrard's elbow on Welbeck was neither. (Though his strike on Michael Brown last year was both
)
As for the first goal, Poll says that the ref got it right to the letter of the law, but was still somehow wrong for not using 'common sense'? What should he have done? Stopped the game? For what reason? 'Common sense' is shorthand for "there is no rational or logical reason for this to be the case, but I feel like it should be so therefore it must." It was a freak goal but it was scored within the laws of the game! Unlike the beach-ball goal, which wasn't. I'd have been livid if it was scored against Liverpool, but it was not the ref's fault.
Why didn't he comment on the first goal? I checked the Laws of the Game regarding offside, it says nothing really just your basic definition -
Offside position
It is not an offence in itself to be in an offside position.
A player is in an offside position if:
• he is nearer to his opponents’ goal line than both the ball and the
second-last opponent
A player is not in an offside position if:
• he is in his own half of the field of play or
• he is level with the second-last opponent or
• he is level with the last two opponents
However, "level" is not defined that I can find. Was he "nearer" the goal? Well, part of his shoulder might have been but his feet and most of his body were not.