Well done everyone on those critiques

Lots of good ideas coming through and we've already got some discussion going on. There are a lot of questions to address so excuse me if this post is a bit long
Firstly, this was my actual thinking in those turns:
Start: worker moves on the off-chance we see some bonus food; he moves onto one of the 3 most powerful tiles, the bgs next to a river. There is nothing to encourage moving the settler so we found: it is always useful to have a city on top of a luxury too to prevent it from being pillaged.
We select warrior first to begin exploring, which is the single most important thing we need to do early on: gather information about what lands are available to us and who we might be sharing those lands with.
Why pottery and not writing? Pottery is more important to us and not something we should take a risk on. What if we have no expansionist neighbours to trade pottery from? What if we have no neighbours period? A granary (on which more later) is the single most important building in the early game; we need pottery to bring it into play. It is also quick to research.
Mad-Bax is correct to suggest this diminishes our chances of getting writing first, but the biggest danger is from huts rather than another civ researching it. The only civs that can research writing from the start are commercial civs. But as Bamspeedy's research has shown, most civs tend to prioritize bronze working from the start. If not bronze, they go after other first rank techs ...the chances of another civ starting with writing are very slim. If we get beaten to it, it will most likely be by an expansionist civ scoring a tremendous run on huts.
Turn 1: worker mines the tile before roading. The simple reason for this is that in the early game, shields are more important than gold.
To address Greebley's point, later in the game (say, Middle Ages onwards), roading before mining is also my preferred option. The reason for this is that if you have a lot of workers close together, roading a tile first will allow other workers to join in the mining without wasting turns on movement, thus speeding up the rate at which improvements can be laid.
Turn 5: first warrior explores west.
There were 3 possible directions I could have sent the warrior: west, east or south. Since there was coast to the north, that would suggest there may not be much land in that direction. Because we are almost dead center in the mini-map, it is very difficult to make predictions on what shape our landmass is. Moving the warrior west wa sbased on the fact that I could see grasslands in that direction whereas south and east wa sall jungle. And in any case, the exploring warriors are fourish turns apart in being produced, so exploring in one direction before another will not make a massive difference.
Turn 7: worker roads the tile. Moving without roading is inefficient, as it means that later you have to waste another worker turn to get back to the tile to road it.
Turn 9: second warrior east. There was not a lot to choose between east and south, either would have been fine.
Turn 12: this is when I popped the hut, for it to be deserted.
I am glad to see that you have all spotted that there seems to have been a delay in popping the hut. There was! Entirely deliberately.
The hut could have been popped the turn previously, but I chose not to. The reason for this is that if I had got barbs, they would have spawned next to the worker, which would have meant I would have had to interrupt the worker to keep him safe. The capital was safe becuase a warrior would have been produced by the time any barbs could have got there, but the worker was not safe. Thus, I deliberately delayed the pop for 1 turn until the next warrior was completed, thus allowing me to protect the wroker and capital if I got barbs [if i had got barbs, I might have interrupted the worker anyway, since a barb warrior could kill our warrior covering the worker, but delaying nevertheless gives me more flexibility and options]. As Greebley's experience shows, early barbs can hinder your growth!
Since the hut was empty, I sent the newly produced warrior south to explore.
I also, as you all noticed, reduced the science rate 2 turns before the end: this is simply more efficient than waiting until the last turn, when you may still have beakers overrunning. At this stage in the game, it makes a tiny bit of difference, but later in the game it can save you 100s of gold. It's a good habit to get into: wait until 2 turns are left on research, increase the science rate to see if you can get the tech in 1 turn (here we were already at 100% so we couldn't increase the rate), if you can't, reduce it to the minimum still showing 2 turns. Adjust again when there is only 1 turn left to see if you can save any more.
And the barracks was, of course, a granary prebuild.
Turn 14: contact with Spain.
As Greebley discerned, we could also have thrown in bronze-working and gained Spain's 10 gold rather than pay 9g. The reason I did not do this was it does not represent fair value on bronze working. The AI very rarely build granaries early in the game, but it does build spearmen, so the tech to withhold is bronze, not pottery. As it happens, Spain got bronze soon after, but the trade made was still the best one at the time.
Mad-Bax: the trade was made because it was a fair trade. How do I know this? Maybe you could think it through...think in terms of what contacts does to tech prices and what different techs are worth....I know the point you're making, but I know that Spain did not have any other contacts when we made that trade, so we got full value for it...see if you can figure out how i know that!

Then we can discuss that point in more detail.
Turn 20: lux to 10% is to avoid a riot since Seoul is now size 3.
Now to address some of the issues that have been raised!