I've been in technology for 20+ years, spent at least 2/3 of it at major OEMs similar to apple. I even helped work with some support queues/logistics when I was at one of them, so I understand how the process works.
This is no poor reflection on Apple, this is how the industry works. 9 out of 10 people calling in for support probably have stupid user-induced errors or simple things that can be corrected. (I once had a woman who worked for me call the internal support desk because her laptop was no longer charging. I heard her berate the internal call desk guy as he asked her to go through all of the steps. She said "I'm an electrical engineer..." Then she realized that while the adapter was plugged into the wall, the plug into the power brick had fallen out....) There is a reason that they go through all of those steps with people.
What I did when I called was follow this set of statements:
1. Explain exactly what is happening. I did not just say my monitor wasn't waking up, I went through a detailed description. I mention at this point that I know there is an issue with the Mini and HDMI waking up monitors. I explain to him that I do not expect a fix, I am just trying to log this for future reference once they have a fix identified.
2. I took them through all of the trouble shooting. I mentioned that I have been working on this for weeks, so that he knows that this is not the first time I have experienced this and he is not the first stop in the solution, he is the last. I went into detail about all the things I have tried. Different cables, different computers, different APPLE computers, to verify that:
A. the monitor is capable of being woken up
B. The cable is capable of carrying the signal to wake the monitor up
C. The mini is capable of waking up the monitor is some situations.
This allows them to narrow down the potential problems. In addition, it shows them that I understand what I am talking about, so they can skip some the the typical user-induced questions.
3. I highlighted this thread and said I had a dozen case #'s if he wanted them for reference. This says "look guys, you have a problem and I am not an isolated incident." This gets me put on hold while he goes to check with engineering. Sure enough, the answer is we are working on this, don't have a fix yet. But I have a case # in there so I am in the queue when they come up with a solution.
Remain calm and cordial, you're all on the same team here, getting angry is not going to fix the situation and threats don't speed up the process.
At the end of the day, Apple is either going to need to fix this in firmware/BIOS, fix it in software (Yosemite update) or replace the unit. If it is the first 2, then because I follow the updates carefully, I will deal with it myself. If it is the third, I want my system registered so that I can follow up for getting a replacement once they finally give in. The problem is, similar to the problems with nVidia GPUs, this could be years away.
Also, I highly recommend keeping a very detailed call log. Time, who you spoke to, how long you sat on hold, what they told you and what you did. I have ongoing issues with my ISP and when I say "this is a problem that started in August of 2013 and you've rolled trucks to my house more than 25 times" it changes the conversation completely. If they tell you to hang up and try something you can say "on January 7th you guys told me that and it didn't work". It puts you in control of the situation. I hate to say it but call centers are managed by metrics, for some it is call handle time, so "try this and call back" helps the agent's metrics. Not saying apple is like this, but once you understand how call centers work, I can start to see how to deal with them.