It is important to note that this discussion of anomalies is written by a statistician, rather than a meteorologist.

What is an anomaly? The OED suggests 'irregularity of condition, an exceptional circumstance, abnormal'.

It has become popular for persons reporting weather data to show an actual figure, and its variance from the average. This is labelled an anomaly, but is it?
The following example comes from a recent month's rainfall data. Variances will be discussed elsewhere, but for now, there is one day in the data that follows which might be considered an anomaly.

May 2007 rainfall:
The total rainfall for this month was 106.5mm.
The average daily rainfall for this month was 3.4mm. ('Average' here means the arithmetic mean, and is rounded to 1 decimal place.)
As no individual day received exactly 3.4mm of rain, comparing any one day with the average will result in a variance.

On day 17 of the month, 2mm. of rain was recorded. This was 1.4mm. below average.
There is nothing irregular, exceptional, or abnormal about that. It if perfectly normal, to be expected, and unless all the data in a set are identical, it is an inevitability. The variance -1.4 is exactly that; it is not an anomaly.

On day 29 of the month, 36mm. of rain was recorded. This was 32.6mm above average.
Surely that was exceptional, abnormal, an anomaly? Possibly. Day 29 was a day of heavy rain. Is it unusual to have a day of heavy rain in a given month? Would it not be more unusual to have several days of heavy rain in May?
Given my location, I would expect a few days of heavy rain in October, and one or two in certain other months generally between October and March. While it was not an enormous shock, I was not expecting a day of heavy rain in May 2007, at least, not to the extent of 36mm.. So, I would have no problem in describing that as an anomaly. All of the other days showed a variance from the mean, as is expected and none were anomalous. Day 29 was unexpected.

If the term is used for every little variance, we miss the few real anomalies that might occur. Rare as they are, that would be a shame.