His PMQs are treated as a joke, and in no way is he effectively scrutinising the Conservative government or holding them to account. Miliband, for all his flaws, kept the Coalition on their toes and actually managed to defeat the government on several leading issues such as Syria. The Labour Party are not performing their role as HM's Opposition to the same standard that they were in the last parliament. In fact, government U-turns and defeats in this parliament are stemming from internal conflicts rather than from the Labour Party's external pressure.
Voicing "the opinions of Bill from Doncaster and Bob from Newport and Jenny from Leicester" is not effective opposition. It's a joke of a way to conduct PMQs that offers no rigorous scrutiny of the government's actions. HM's Opposition is supposed to be a government-in-waiting, not the voicebox of Pat from down the road. Sure, they express genuine grievances, but the way in which Corbyn presents them simply undermines his entire point.
Membership has no baring on electoral performance. In fact, many of the individuals who support Corbyn and joined in order to vote for him and/or participate in a Corbyn-led Labour were most likely either Labour supporters or Green supporters anyway, and have joined simply because Labour is now more in line with their views. I doubt that it represents an increase in the appeal of the Labour Party nationwide.
The 2015 General Election reduced Labour's share of constituencies back into its electoral heartlands (with the obvious exception of Scotland), meaning that in order for it to make gains in 2020, it needs to appeal to the voters of marginal constituencies outside of Labour's strongholds. Those voters, funnily enough, are the ones who are turned off by the sort of policies and tactics of Old Labour. Labour is talking to itself with the kind of policies it's advocating at the moment. You have very little chance of winning over the constituencies that you actually need to win in order to succeed in a general election, and on top of that UKIP is eating into your vote in your heartlands -- which could provide potential openings for the Conservatives when combined with the upcoming constituency boundary changes. I've been saying this from the very beginning, and warned against an 'Old Labour style' leader for the Labour Party long before Corbyn was even suggested as a possible leader.
I'm willing to go into this in more depth if you like, although I'll have to do it tomorrow when I'm not tired.