I've only got a few weeks of experience, but here's my 2 cents:
1. Vials are sealed, right? So when you try to pull out 300 units all at once, you create a giant vacuum inside the vial and end up with bubbles inside the syringe. Injecting half a syringe full of air into the vial first makes it a lot easier to get the full 300 units out without a big bubble problem. Also, once your syringe LOOKS full, tap it a few times and (while still poked into the vial) push a few units back in to make sure if you have a bubble, it goes back into the vial. I don't usually see a bubble with my eyes, but I regularly push one back in when I do this. I think they get in between the needle part and the syringe, but I don't know how that happens.
Also helpful, once you're done filling the resevoir/cartridge, take the plunger out of the syringe and poke it back into the vial (right side up, hold it right side up for this part) so the vial can equalize pressure and the next round is easier to start.
2. I also have tiny bubbles in the first part of the tube, and I figure that as long as they stay there (and so far they seem to), they're a non-issue. If insulin can and does get past them, then they aren't in the way or turning into a bubble-bolus.
3. Apidra and Tandem don't get a long very well. There's a good article discussing this very thing on Diabetes Mine today. There's no great answer to why, and it doesn't happen with everyone, but in general, don't mix apidra with a t-slim. Novolog and Humalog both seem to fare much better.
3. Although I understand being so high is frustrating, waiting only 30 minutes for a correction check isn't very long, most sources I've read say to wait at least an hour, although some of that used to be in order to prevent stacking corrections, but the other part is that insulin just doesn't work that fast in general. On a related note, it can depend on what caused the high... if its from 4 hours of missed basal due to a bad site, and assuming a 3 hour active insulin time, then it will be 3 hours AFTER plugging back in that the time-lag from all the missed insulin is over. Frustrating, yes. Lastly and most unfairly, you know your glucometer only has to be within 20% to be considered accurate? That means a reading of 350 could really be 420, and a second reading of 350 could really be 290. Not helpful, but keep in mind that especially on the higher end, numbers are not very accurate.
That its happened 3 times in the last week though, thats suspicious. Although might be very closely and directly related to....
4. Infusion sets! There's a billion different kinds out there, so if you have one you hate, get a different kind. Curses to MM for their "proprietary connection" system, you can substitute almost any other brand, EXCEPT theirs. Here's a good comparison chart between brands: http://www.diabetesnet.com/diabetes-technology/infusion-sets (any that have a "luer lock" connection will work).
Most supply companies will let you exchange unused sets, and many will send samples too so you can try a few out before ordering a whole box.
I personally really like the cleo sets, I think sticking the tape first and then stabbing the needle is much friendlier than shooting the tape and needle together, and at least for me, it seems to make a more stable insertion because the tape is already stuck to me. My common problem is that things stick too much, and I get a big rash though, so maybe that I like these means they are a little less sticky? If they worked for everybody though, there wouldn't be so many options! If you still can't find any that stick, you can look into skin prep and similar "tape helping" stuff (skin prep, mastisol, etc).
My guess, having just gone through my own "adjustment period" (new pump, new tools, new sets) is that the high BGs are a combination of problems, and with more time and tricks up your sleeve (sticky stuff for sets, air in the vial) some of them might go away and you'll be fine. Talk with your endo/physician/CDE about Apidra though, and call your supply company about new sets. And, always call Tandem and report problems even if you don't know what caused them, because if they don't know what we're getting stuck on and stuck with, they can't improve the next version or issue better advice.
Lastly, there's no law that says you have to struggle through with a new pump if the old one still works. I didn't get a long with my MM system, so I was very happy to upgrade, and for me the first few weeks of trial and error were well worth it, but if it isn't working for you, there's no reason to force the issue.