One can set up some pieces and concoct a situation that has, say, a mate in 3 (yes, I know it is not straightforward, but if you sit for a few hours you can do it).

Such problem would probably not be accepted for a competition because the modern standards are already too high. There has to be a relatively original idea and/or theme, but I do not know what qualifies as mediocre these days, and what qualifies as novel.

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    Late Addendum: "Modern Standards"...those standards have changed a lot in ~200 years of problem chess. Even fads exist. Standards are bound to change again. (And yes, they are high.) – Hauke Reddmann Aug 28 '16 at 19:57

One might simply look at the judging metrics at the World Chess Composition Tournament (WCCT) to derive such an answer.

This is from their Rules Annex and details how points are allocated to a composition entry. I've stressed key words that probably represent a figure of merit.

Points : Description

4.0 : An outstanding problem: an accurate and intensive rendering of the set theme, without blemishes in any of the main lines, and showing originality and flair. Perfect construction and economy.

3.5 : As above, but some small constructional weaknesses, and perhaps not ideally economical.

3.0 : Either: a very good problem showing the theme clearly but perhaps not intensively or very originally Or: a task rendering of the theme which does not reach the highest artistic standard. In either case, good construction and economy.

2.5 : As above, but constructional weakness and/or less than ideal economy because of the intensive or task setting.

2.0 : A good problem, very likely worth an honourable mention or commendation in a reasonably strong tourney, but not a very intensive rendering of the theme, and perhaps not very original. Adequate to good construction and economy.

1.5 : As above, but with some artistic weakness or constructional blemish.

1.0 : A very ordinary piece of work, typical of many average columns but hardly up to award standard. Adequate construction and economy.

0.5 : As above, but with serious constructional defects.

0.0 : Unsound, unthematic or fully anticipated.

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Quote from our Autralian friends http://www.ozproblems.com/problem-world/chess-problem :

Problems are aesthetic works designed to show an interesting theme – the composition’s main idea. How exactly are themes artistic? It varies, but important factors include subtlety, elegance, economy, paradox, and unity of play. The latter concept of unity is especially noteworthy; most good problems have multiple variations that are related to each other in some way, to create a harmonious impression.

The metrics provided at the World Chess Composition Tournament (WCCT) concern a formal tourney where the problems must all present the same theme that is imposed to all participants. This is why the Rules emphasize the "accurate and intensive rendering of the set theme". However, in informal tourneys (generally composing tourneys organized by chess problem magazines), no theme is imposed.

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