Does typical duration of Short Term Memory differ between tasks? The duration of Short Term Memory is a fuzzy thing; Wikipedia notes several disputes over it's length and I recently alluded to this fuzziness myself.

However, I wonder if part of the apparently unpredictable duration is to do with the different types of details we remember. For instance I find it very likely that context-rich information such as where I left my car keys (many related cues exist in the relevant location to make it recognizable) likely persists longer than fairly arbitrary data (no relevant cues typically exist, except perhaps area code).

Experiments typically only focus on a single task or related tasks to measure short term memory. Is there any evidence that indicates different short term memory tasks have different "forgetting functions" or time until a specific percentage of the information is lost? 

Tasks I'm thinking of are basic memory tests like remembering lists of words/numbers/letters, remembering parts of a story, answers to a quiz; ideally things with different sorts of modality or potential for Chunking.
As you pointed out, the duration of short term memory(STM) varies and there are different theories.   However, in mainstream opinion, ideas or thoughts classified as "short term" are said to decay after a short amount of time (minutes at most). If an idea is recallable after a few minutes (or even a minute) then it would be classified under "long term memory" (LTM). Your example of leaving your keys and then later remembering would be the following process: You leave your keys and the act is stored in your working memory and through special attention is encoded into LTM which you later recall while looking for your keys. Further, if you are using "retrieval cues" then you are attempting to "retrieve" it from your encoded LTM. So if a cue reminds you of something then that "thing" was already encoded in LTM. So this "keys" example and examples involving "remembering lists of words/numbers/letters, remembering parts of a story, answers to a quiz" are not short term memory issues at all but rather encoding and LTM issues. 

So if your question is "Does the chance of encoding from STM to LTM differ between tasks?" the answer is yes.

You do have a greater likelihood of encoding certain short term memories over others. This is generally because you have a vested interest in an idea or it has an attribute that is distinct from the others. For example: if I listed "apple, banana, orange, house, kiwi, mango" then you may pay special attention to "house" because it is not a fruit and thus different. Because you pay more attention to this it has a greater chance of being remembered. Interest also plays a part. If you obsessed over something (let's say ponies) and that word or an associated word (e.g. pony) appeared in a random list then you are more likely to remember that word than the other, less significant, words. It has also been shown that on average people remember the first word in a list (primacy) and the last word in a list (proximity) than any given word in the middle. Lastly, of course, there is a greater liklihood of remembering something if you try through mnemonics such as you mentioned (rehearsal and chunking). I hope this answered your question. I also hope I didn't misunderstand your question.