and I check the trend for 'All Time', it looks like the rate of growth in the number of bitcoins INCREASED around January 2010. I thought that the rate of growth (enforced by a computer algorithm) would halve every 4 years and that it would never increase... Am I missing something?
The rate of bitcoin production is set so that on average, regardless of how powerful the network is, a block should be discovered every ~10 minutes. If the network becomes more powerful due to new entrants to mining or better technology, the network will adjust (after a short lag time) by increasing the difficulty - and the same process would work in reverse if people left mining or the hash power dropped for some other reason.
The fact that the # of bitcoins per block halves sequentially doesn't really apply as much as the difficulty targeting which would still happen if bitcoins per block never halved again.
Because of this, we see a linear growth in number of bitcoins mined while network hashing power increases geometrically. All this means is that your 5GH/ps Jalapeno is already obsolete and by the time you get your 600GH/ps Monarch delivered in April or May 2014 it will already be nearly obsolete.
It is decreasing by half every 4 years, just that graph is just not showing it well for this short timeframe.
The dip up until 2010 was due to there only being one or two miners in the entire network, so the maximum number of Bitcoin wasn't produced in that period. The speed of the entire network couldn't keep up with the minimum of 6 blocks an hour which has lowered the total available Bitcoin in that period, though the number overall is just fine. You can see the sharp decrease in late 2012 when the block reward halving first occurred, which is the start of the downward trend in block reward production.
Currently the network hashrate is increasing so quickly that it's producing more Bitcoin than expected, we'll probably reach the next halving in a little less than the intended 4 year cycle. That's not a negative effect in itself though, it just means the network is increasingly secure month on month. There's a similar hump between June and July of 2011, when GPU mining was publicly introduced.