Non-stacking is because there are two types of tree trunk, those cut during rain/snowfall and those not cut in rain/snowfall. (This has to do with a certain quest). There are no actual quality differences between them (although the quest makes claim one type is better than another for making punts--not exactly relevant when punts are not a player-craftable item and all that)
At current time, there is no risk of trees falling on you or the likes, though there are plans for such things to happen in the future (per the Developments page on-site:
http://www.unrealworld.fi/urw_development.html, section Skills -"Special consequences from failed attempts to use certain skills; e.g. hitting your knee with an axe when felling a tree etc." - though there is no predicted timespan in which such changes will happen)
For some parts of timbercraft--splitting trunks into boards, since boards do actually have quality modifiers--I believe the message has some impact on quality. My suspicion has also been that it has some influence on the average time needed to complete such a task, but I do not have solid proof of this nor have I extensively tested to verify this suspicion; it may well be that my impressions are merely self-reinforcing.
There are other contexts in which such a message--or its variations regarding the other penalty stats (injury & weight carried) or a mixture of those--displays, in various degrees of severity (other than "prone to succeed poorly", there's also "slightly disturbed", for one, and some stuff in between). Setting or retrieving nets while carrying significant weight, for example.