My own experience:
I do not have a standard checklist.

I usually check the first sets of shop drawings with a lot more detail. Once I am satisfied that the detailer is doing a good job (most of the time), relax the checking quite a bit. I concentrate on making sure that no reinforcement has been missed and that the quantity, lap lengths and configurations and diameter are correct. I usually do not check lengths.

The layout/style of the shop drawings does not bother me. In my view, the shop drawings are not produced by me, but for the fabrication and installation of the reinforcement. The site check is always done with the design drawings (in my projects design drawings have always had quite a lot of detail on them).I also have the same people who check the shop drawings doing the site check. It helps a lot, they become very familiar with the reinforcement and the process becomes very smooth.

I do not mind phonecalls or e-mails (e-mails more common these days), in fact I think them positive. I like it if the detailer catches errors or comes with alternatives that are easier to place on site, designers do not always get it right.I only require RFI for substantial changes. For small changes, the shop drawing approval process is enough. I might make a note on the drawing next to the detail saying something like 'detail acceptable' or 'change acceptable'.

I do not mind suplying autocad drawings, they are sent without the title block and the detailer signs a disclaimer, but I do not see the point of people working twice, and if I can help the detailer make a bit more money and work less, all the best. It also reduces the scope for errors (assuming design drawings are right).

Not only detailing, but every single process on the construction industry is speeding up these days, so better get used to it. Reasons? money of course, the more you can compress the construciton period the more money you can make. Also, traditionally, the whole design would be prepared before construction tenders were out. These days many jobs are tendered only with conceptual or general designs or they are design build.

If you have the chance, I would suggest, and what I do, is that for every job you have a meeting (better) or a telephone conference (not so good) to discuss procedures and all these issues you just asked about with the rest of the team. Different people have different styles, and if you set up the rules of the game in advance, there is less scope for problems.

I would say that most people would be happy to talk to you.

Sorry but I would rather do not provide examples of shop drawings, they are not mine but the detailers'.

My checklist would be my signed and sealed drawings you used to create your shop drawings.  Excellent shop drawings are 1) correct, 2) show where the rebar is going and 3) can be read by anyone that might be using them.  

My job is to give you drawings that clearly show where all reinforcing goes on the job.  If I don't do that then you should send an RFI through the Contractor (or your client).  

I don't mind calls but you should always follow up with an RFI.  If you are receiving bad drawings then flood the engineer with RFI's.  Then maybe next time they will create a better set of drawings for you to use.
 

I am a rebar detailer of 15 years. I agree that typically, in such an environment as you mention, you become the product of your environment and training of the past is repeated. You can not tell if new ideas are accepted or practice, just what has been done.

So when something is new, see what others in your office have done before but than check the following. First, check the ACI and CRSI handbooks for methods and correct presentation or representation. Although the diagrams may seem antiquated, its a start. Second, find someone outside your firm and bounce ideas off them if the question comes up on how to approach a job that is new to you. That is what I would do.

Regarding checklists, it depends on the engr and its company policy. Some do have lists, others don't. Likewisse, some engr have people who specifically check placing drwgs, not the actual designer. I have even seen the drwgs outsourced for checking review. It is like the extent of the review, some are rubber stamped reviewed  while others are highly critical. Sorry, no answer there. It greatly varies.

Fast track construction is here to stay. It is typical for updated drwgs as progress is completed. Sometimes it is in result to what is found on site, some to redesign by client of engr. There are lots of reasons for it. Best recourse? Keep adequate notes and file system regarding new and old drwgs. Push you clients to take delivery as needed. They like to have material on site and ready to go, however, if you can see a job changing like this on the fly, advise it is in the best interest to hold off until absolutely needed to counter revisions.

Experience shows that often missing dims are typical. If something is missing, give it your best estimate and move on. Show only dims you are unsure of and put on drwg to verify. Than if incorrect, you can reference back to verification request. Also, while you may place dims with the engr or arch, the gc could be the party reqd to field verify due to conditions. They are not exempt.

CAD files are touchy. Some will, some will not. You can get in the habit of requesting. Worst case, they say no. Regaring questions, start thru GC first. Some people are touchy on the chain of command and proper channels, standard protocol. Mainly, as a paper trail to CYA. But if you do get to talk to the arch or engr, ask if acceptable to call direct. As with CAD files, some yes, some no.

Hopefully that helps you a bit.