The river direction is not 100% correct. Please check the direction on upload and change if necessary (if you know which way the river should flow). Use common sense - A river connected to a coastline should normally flow down to the sea ;-)
Do your best to determine if the feature is a stream or a full river and set at waterway=stream or waterway=river as appropriate. Comparing to Bing imagery may help. An arbitrary distinction between the two might be a stream is something you could jump or stepping-stone your way across. Rivers generally you'd need a swing bridge to get across, or rope yourselves together.
Names for rivers are often found in nearby descriptive text nodes.
Check for them (they show up loudly in JOSM) and attach as needed.
RP: there is no 'sloppy' tag. all data is valid; accuracy is contextual to a given situation. if someone feels like updating it to become more accurate, they will. i would suggest using "LINZ:river_definition=indefinite". or, some people add a note=tag, with a wordy explanation for situations like this. e.g. "note=needs GPS"
HB: indefinite is not used in the Chathams; river direction seems random. That's not easy to fix without a lot of GIS'ing unfortunately so we'll have to live with it & let folks fix as they go.
RP:regarding the direction of the way: would it be possible to compare it against a db of contours/spot heights, to find out which end is highest?
Yes, it's possible. We'd need to build a raster DEM from the contour+height_pnt layers though at ~ 10m grid resolution and take spot heights. Then you'd have to write something which reversed ways based on height A>B for that segment. It's possible, but a fair bit of work and can be done after the upload.
Uploaded for Chatham Isl 14 May 2010 (Pitt uploaded earlier) (HB)