When looking at a web site like that it's a good idea to compare what they show for a few other cars, ideally cars whose track record you know. For example, years ago when I decided to replace a defective GM product with a Toyota I looked at that site and found quite a few complaints about the Camry. Then I looked up my then-current GM car and found something like 10x the complaints about it, and generally of a much more serious nature. 7 years and 120k miles later the Camry has been basically problem free except for normal maintenance.
The early LEAFs did get a lot of complaints about grabby brakes. You'll also find a number of complaints about the resistance heater, which needed to be replaced in a number of 2011 and 2012 LEAFs. The 2013 and 2014 LEAFs are built in Tennessee, not Japan, and there were a number of mechanical changes which resulted in complaints about the on-board chargers and again about the heaters, but a different problem this time. AFAIK both of those have been resolved for some time. Having said that, many people who had both a 2011 or 2012 LEAF and a 2013 or 2014 LEAF have posted on this board that the Tennessee LEAFs don't seem up to the same quality level as the Japan LEAFs - mostly minor issues.
The biggest complaint by far was the rapid battery degradation, and members of this board have done extensive research on the issue and took it up with Nissan, which provided a extra battery warranty in response. The whole sordid saga is described here:
http://www.electricvehiclewiki.com/?title=Battery_Capacity_Loss
You can read for yourself but the short summary is that:
1) Under extreme heat conditions the battery degrades extremely rapidly. People in hot climates like Phoenix saw their batteries lose as much as over 1/3rd of capacity in just 2 years. People in mild climates such as Seattle are experiencing much slower rates of battery degradation.
2) Even in mild climates, however, degradation has been somewhat faster than Nissan forecast when the 2011 LEAF was first made available. 20% degradation was forecast for 5 years and it has been more like 3 years - although this varies greatly depending on the situation, as is noted at the above link.
The other issue generating a number of complaints has been cold weather range, and in general advertisements about range. In 2010 the LEAF was advertised as being a 100 mile car, and the 2011 marketing materials included that figure, although the test used to get that number was under ideal conditions. The EPA rated the 2011 LEAF at 73 mile range, which is a pretty good estimate although literally YMMV, and the range varies a lot depending on a lot of factors. The 2014 LEAF is EPA rated at 84 and that's probably a bit on the optimistic side in *most* cases, thought it is certainly possible under many conditions. However, a lot of people bought assuming 100 miles - and a few dealers still claim this figure - and so many buyers have been very disappointed. Add in the fact that range can be reduced by 50% under extreme cold conditions and a LOT of LEAF customers were posting complaints on line last winter during the cold spells.
Personally I've found both our LEAFs to be extremely reliable with minimum maintenance (basically just tires) - one of them did have the heater issue which was resolved under warranty. But do be aware of the range and degradation issues.