Posts pulling out of the ground probably won't be a concern (that roof looks real heavy), but, depending on how windy it is there, you never know. It looks a symmetrical structure, so torsional effects may not be a concern either, depending on the site. I was just throwing out some of the things that popped into my head, some of which may or may not be relevant once investigated a little bit.
Timlocks are what we call those screws (at least around here.) They are great things, and, have a lot of uses in a modern timber frame structure. But, when loaded in shear, there ulitmate capacity is function of how big the shaft of the screw is, and, they tend to be fairly small diameter (1/4" ish). They hold things together in withdrawal real well though, and, provide some clamping when they get screwed together.
As some folks have already mentioned, a lot of the weight of that structure is in the overhang, and, if there was an additional piece of wood between the two dimensional lumber braces to provide direct bearing of that hip, you would only be relying on screws at the heal, which could make for a much better scenario.
As far as the corner connections, it may be adequate. Having the stub of the post run by is the saving grace though. Lags into endgrain tend not to be a great connection, and, isn't doing a whole lot in this case. But, screws into the stub are a good way to go. Helps tie everything together, and, certainly helps transfer any uplift from wind to the post if that is a concern. An additional screw down through the lap connection to tie the two together there may be well spent.
But, otherwise looks good, and, I'm sure you'll figure the rest out.
Joe
