The NOLS outdoor leadership school used to (probably still do) use them for 30 day trips in Alaska. Leaders would often do back to back trips, so would spend most of the summer drinking iodine water. I have personally used it on 5-7 day trips many times. Never heard of any long term issues, but maybe I've missed something. Also most people are getting iodine from their salt as a supplement.
This from a peer reviewed journal:
"The strongest data suggest that low levels of iodine (1-5 mg/day) are safe for most people for years. It should be noted that Freund et al. (48) supplied 1 mg/L iodine in water, not 1 mg/day, and estimated the average daily intake as 2-4 mg/day. Well-controlled experimental trials have evaluated intermediate levels of iodine from 10 to 32 mg/day for up to 3 months. These levels consistently cause subclinical changes in thyroid function, and may cause thyroid enlargement, but clinical hypothyroidism was not observed. The data from Georgitis and McDermott (53) and LeMar et al. (54) suggest that 3 months of moderately high levels of iodine ingestion (32 mg/day) carries no more risk than 1 week of ingestion."
http://ehp03.niehs.nih.gov/article/info:doi/10.1289/ehp.00108679
If you use the recommended dose (2 pills/L) from Potable Aqua, you would get about 16 ppm or 16 mg/L (assuming I did that math right). I use half that dose for about 8 mg/L. The manufacturer recommends limiting use to no more than 6 weeks at the full dose, so I think you are good.
I do prefer to use the neutralizer before I drink it just for taste reasons. The neutralizer essentially counters the oxidation effect of the iodine by adding an acid (absorbic or Vit C) to the mix.
Another perk of having iodine in my opinion is the ability to make a clean water with slight oxidizing properties for cleaning out minor wounds.
Yk