Trimble compensator issue/calibration

Running the calibration routines yourself is not a problem and I wouldn't trust a dealer who told me it was. If your compensator is working correctly, you can be out of level by a significant amount without losing any accuracy. That is the whole purpose of the compensator. Most trimble access routines will not allow you to take a shot when the instrument is out of level beyond the range of the compensator.

I'm in a similar situation and I have to say that going from Leica to Trimble is not a pleasant experience, especially when the gear isn't exactly new.

The DR shots are very inconsistent and I always have to check the distance to make sure it's not reading to something random.

I haven't even figured out how to read two-faces and I'm not sure that would help with the quality of the equipment I'm using (old poles, old legs, tribrach that never aligns with the e-bubble). The only real upside is the increased battery life and range but pretty much everything else is worse.

I'm trying to learn my way around the instrument but it's not very straightforward, especially with the prescribed methods by the workplace. I get a headscratcher every other day when I ask a question and get an answer that is so painfully wrong but espoused with such confidence that I am left dumbfounded.

For the record, I'm a long time Trimble user that has (relatively) recently switched to Leica. 

I'm not real clear on what you mean by "align(ing) the compensator on one side" or the other. Nevertheless, I second Lurkers comment that collimation is a user level thing, not a shop task. That goes for all makes and models of total station. So, collimate and see if that doesn't fix things.  It's a 5 minute in the field thing.  And get somebody to show you how to double angles. It's not that different from the Leica.

One more thing...... you haven't mentioned what models of instrument and data collector you are using and have experience with. Trimble has several. It really helps to know that when giving specific advise.  

I have had tech support from a trimble dealer tell me to not adjust.

I still do.

For DR aka Reflectorless, Trimble is far inferior to Leica in that department. Same goes for the S5 at shooting sticky targets, but the S7 and 9 can tell the difference between a nearby telephone pole and a sticky target at least.

I have used both and prefer Trimble. The DR mode in Trimble is not even close to the Leica. Leica has a very slim narrow beam. Trimble s series and there basic total stations non robotic are not very good for using DR for precise work like Building corners etc with DR based on how far you are from a building corners etc and the angle in which you are to said building corners. The beam gets to wide and can cause you to be out. Also same goes for shooting through a small hole in trees briars. It starts reflecting off of limbs etc. as it gets further away from the gun.  You have several options on direct and reverse.  Also if you want angles only or a distance in face 2 as well. One is in the measure rounds routine. If you want a direct and reverse on say a stake out point or a Topo point and it’s just here and there not all points. If you are running Trimble access or the older version of it called survey controller. On the bottom of map screen there’s an option soft key you can add that to it. If it’s for all shots you can do this in the survey style. So say I was setting anchor bolts. I might start with setting my station via a station plus set up and observe both backsights in face 1 and face 2. Then I would set in my survey style for stake out points face 1 and face 2. I might also add I might have it in tracking mode for the edm so it’s continuously shooting until I am very close then I would switch to standard mode so you would have to hit the button to measure a little slower but it’s more precise. 
you can google the Trimble information and there some documentation on the DR beams that can give you an idea on how that works the math behind the beam divergence. For most in total stations and robots they have. One exception is the SX12 now that beam is more equivalent to the Leica very small and tight. I will try and upload tomorrow some docs for you if you let us know which instrument exactly you have and software. If it’s not to old you should have a help menu right in the data collector itself. Any routine you are in say a cogo compute point and you launch the help menu it automatically goes to that exact topic on the fly for you. I have s5 s7 robots also the C5 or something total station. I have the DR docs already downloaded for those. The c5 total station is like a beam divergence of around 35mm at 100 ft or something crazy so it’s fine for shooting a power pole across the street but not good for building corners. But Trimble accepted has lots of power and neat tricks to do many things.  You just have to wrap your head around what it’s as for and make some changes to your process to truly get productive.  But once you get it man you can calc and do things so smoothly. I don’t think there is anything I have come across that I have not been able to compute in the field. As a matter of fact I keep an emulator on my desktop in the office to do comp checks with many times vs other things like cad because it’s just so easy. Or if I am cheating a set of plans to make sure someone else’s comps. I will use that. Or my old hp48 with SMI. The biggest problem I have seen especially when I was a trainer many years ago for Trimble was people were trying to use it exactly like they had in the 80’s. Data collector routines. I have seen that same thing happen recent years and once a few procedures are changed and such then the time savings is huge. Especially when using the office software Trimble Business Center to do all the qa/qc and adjustments in. Before points go off to cad etc.