When you are faced with a situation of a leader (subordinate or senior to you) with questionable leadership, how do you cope/deal?

Personally, I see questionable leader actions pretty often. As a SPC, there is little I can do. I can't correct them exactly. Sometimes, though, depending the leader, I can ask a few questions or try and see things from their perspective. Maybe this COA was what they thought was best at the time. Maybe they didn't have all the answers and was forced to make a judgment call. Or perhaps the order didn't come from them at all and they were simply passing along information.
In any case, I have learned a lot from leader mistakes over the years. When I see it happen, I always look at the situation and ask myself what I would do differently. I believe my empathy for soldiers is due, in large part, to questionable leadership I have witnessed.
A LTC is just as human as the lowest PVT. The difference (besides military title and rank, obviously) lies in time, maturity, and experience. We are all just an accumulation of life experiences. I think the most important thing we can learn from both good leaders and bad leadership is what we can learn from each.
If a SSG gives a me a completely ridiculous line of BS, well, unless he's about to get me hurt, I do what he says. This isn't to say that I'm not constantly turning over in my head the "who, what, when, where, why, and how" of it. And trying to learn from it, so that, frankly, I want to try and avoid making the same mistake in the future.

I have some experience in this area with a junior leader I had to fire from their position. The man was a good guy who as an E-7 was more content with being one of the guys. I counseled him, gave him plenty of tasks to do that would insure his success - which he just failed to do, started counseling him monthly and giving him simple goals such as conducting an alert roster test, squaring away the equipment locker and doing inventories on soldier's issued equipment - simple down to earth PSG stuff that he just didn't seem willing to accomplish. I wasn't overly pleased by this guy but I gave him every benefit of the doubt I could. This went on for 8 months until the straw that broke my back was him showing complete disregard for instructions. I was the acting commander and we were at CP Edwards, MA for the weekend. We got in around 2200, he was the senior NCO at the time, and I expected him to get the Es settled in for the night and have the company standing to in formation at 0600 for chow. At 0605 he and the company are still in their racks and I'm standing there trying to explain this to the BC. I took him aside, quietly, relieved him of his duties and fired him as my PSG. Luckily because I had all my counseling statements, I's dotted and Ts crossed, the CofC had no issue with my action after interviewing him and reviewing the paperwork. The guy resented me for the next 6 months until he was kicked out of the NG for getting into enough trouble with civilian law enforcement.

"Embracing the suck" and being patient are important, as you do not want to butt heads with a superior and compromise your position (maybe you are holding the moral high ground, or you are more MOS proficient). Being technically and tactically proficient can help you avoid some BS. For example; your leader wants you to set up a piece of equipment in the field which will be a pain, or is incorrect, etc. If you can recommend a better way based on unit SOP, FM, or TM that will make your life easier and fulfill the mission, then try to do so tactfully. A lot of heartache can be solved by providing a recommendation with supporting documentation for why you are making that recommendation. Tactfully, of course.

I'm in a similar position (newly-promoted E-7 as our PSG, new to the position, needs technical and tactical guidance). I've already had to butt heads over some minor stuff, but with a deployment coming up soon life will be hell if this continues. I've been thinking about it a lot, and the best option I can think of is to try and upwards mentor him. I'll lean on our 1SG to lend his guidance and help develop him (fortunately we have an excellent 1SG I can count on to do so), while I help bridge the gap at platoon level. My concern is that we have a new 2LT coming, and two green leaders at the same time at any echelon is asking for trouble... It was hell overseas last time with a green CO and 1SG.

In your situation, could you cite a specific example of when your leader enforced a standard on you and then you witnessed them violating it? Are we talking violations of our values, SOP/MOS type stuff?