First -- and in case Petra or someone near her reads this thread -- let me say upfront that the reason I am a Petra fan before all other players is that she has the most complete game I have ever seen. So it's not like there are many shots that she doesn't do well. And indeed, the things I list below are shots that she is actually fairly good at.
1. Overheads. I don't really care that Petra has whiffed on overheads before. That can happen to the best. Federer has done that. But it seems to me that Petra could improve her backpedaling, scissors-kick overhead. This is the Pete Sampras shot that made him so difficult to lob. If you have a fearsome overhead, not just a good one, players will be afraid to lob you. Given Petra's big wingspan, they will also have trouble hitting passing shots. A really good overhead would make Petra all the more intimidating at the net.
2. Lobs. I'd like to see Petra improve her topspin lob. It could have been used effectively to punish Errani for the net-rushing she was doing. In the event, Petra made an adjustment and started hitting angled returns past Errani, and dipping returns at her shoelaces. She was then very impressive in her ability to pass Sara off the resulting sitter. She moved well and got in great position to blow a passing shot past Errani. But if she had a better lob, she might have been able to win those points a shot earlier. Also, a good lob is often a great shot to hit and then take over the net yourself, which we all know Petra loves to do.
3. High forehand volley. This is IMO the toughest volley in tennis, and the one that is most often missed. Petra sometimes misses it. I think we saw her push one long or wide against Errani, and another against Caro. Again, she's not bad at it, but it would be great to see her improve it.
4. Body serve with kick. Petra does this sometimes, but she could be more effective with it. A jammed opponent is likely to give Petra a killable second ball -- that is, if they even return the serve at all. The lefty spin of the serve makes it even more likely that a jammed opponent will simply foul it off and commit a return error.
Good intro and list Mac.
Historically, the toughest shot Petra usually hits (or doesn't hit actually/misses the most), is the waist level baseline forehand (usually from an opponents deep looper, lob or high ball, that Petra has to step back from), and swing low to high (i.e. reverse windmill). She usually always hit this ball out, even with a wide open court.
So far in Doha and Dubai, I haven't seen her miss this shot, so hopefully, this is/was a thing from the past.
Last year, Petra was also poor in her defensive slices and bunt/slice/chip ROS. This failed Petra miserably in her Sharapova matches, especially at the Aussie Open, where she could/should have won. However this season so far (obviously/especially Doha and Dubai), Petra's seemed to be executing both shots much more effectively.
Let's hope it continues.
PS: And as you mentioned, Petra's defensive lobs, could use work. Ironically (or maybe, not surprisingly), Petra's usually a little better, when she sets up the lob, off a drop shot ('Petra's so offensive, isn't she'), though that could use some fine tuning as well.