Okay- Have gone back and watched highlights.
On the Connolly goal, Kuznetsov is coming down the wing with Rask on the post watching him. As the pass goes across to Orlov in the middle, Rask is forced to slide back to the middle and Orlov makes a great quick pass back to the side to Connolly. Rask slides over to angle the shot and Connolly makes a nice play to cut back against the grain. You're correct that he stumbles at this point (loses the edge he was going to push back across with?) and has to lunge horribly at Connolly skating free across the crease. I think Rask played it about as well as he could have, barring the slip/stumble when Connolly cut back across.
https://www.nhl.com/video/connollys-slick-backhand-tally/t-277350912/c-48978003
On the Ovi goal, I think you're right. You can see him fighting through the screen earlier, and that is an Ovechkin shot, but he wanted that one back. Slipped under his glove, but you're right- his reaction tells you the story.
https://www.nhl.com/video/ovechkins-snipe-beats-rask/t-277350912/c-48977803
On the Backstrom goal, I think the shot was not quite as hard as I thought it was, but it was perfectly placed and it was pretty quick and that's where rebounds go on that shot. You know this- it's why we put a shot low on the far pads when coming in from a bad angle. I don't think there's much that Tuukka could have done differently. It's on the pads so it's almost impossible for him to corral it. Maybe the move is to let the rebound sit there, but I think most goalies try to kick that away. And his teammates were idiots on that play.
Reviewing, I'll amend my thoughts and suggest he should have had Ovi's goal. I guess maybe he should have been prepared for Connolly to cut back across (or not slipped?) and should have not kicked out the rebound (?), but I think the defense was far more to blame on those two goals than Rask.
Of course you're just a bender and I'm far worse than you. Maybe @realness could weigh in?