Your first point is very well taken - we also urge caution in drawing too many conclusions regarding an overall trend in mean temperatures. However, I think our conclusion - that we are having more hot outlier days now than ever before - is interesting in and of itself.
Your second point is an interesting one, and I too would be curious to look further into the correlation between proximity to a city and temperature. However, to look for outliers, we created a long-running distribution of seasonal temperatures for each station individually - so in some sense the map is already corrected for this effect. Each anomaly you see is an anomaly for that station alone - meaning if an urban station regularly gets higher temperatures than a rural one, it will take a proportionally higher temperature to trigger an anomaly on the former than on the latter.
Furthermore, NOAA has been good about getting good national distribution of these stations so it's less of a concern than you might think.
That said, urban stations may still show artifacts compared to rural ones, eg. when there is an extreme warm outlier, cities may be more likely to have another warm outlier the following day due to the heat storage effect you mention. I'm not sure.