laxman888,
Thanks for posting your game (it makes it much easier to dissect). No problem with the Mac <-> PC conversion.
In terms of "basic mistakes" to me the one to highlight was that Iron Working was not discovered until 125BC ... you have arguably the most influential unique unit in the game, and it's a Golden Opportunity gone missing to have a tribe with this great unit and then wait for so long before building them.
A 'common' Roman strategy is to race towards Iron Working, find where the Iron is, hook-up near or even settle on the Iron, and start churning Praetorians out. Get a SoD of seven or eight with a few Axes and Spears, and go 'kick some behind'. After four or five cities (more because you're on a large map) the city maintenance will start to hurt your spending on science, and you'll be well served by pillaging and razing the enemy cities rather than capturing (... most of ...) them. Keep churning out more Praet's as reinforcements. In this game you have Tokugawa as a neighbour - he should have been smashed centuries ago with your Praet's as he will do absolutely nothing for you in nine games out of ten except present himself as an enemy (or present himself as a builder of your future cities

).
Did I mention "city maintenance"? Two technologies are important here - Currency and Code of Laws. These were acquired in 1110AD and 960AD respectively - far too late for you to support large expansion while leveraging your Praetorians.
There are other and lesser aspects to your game that I'm not sure that I'm quite following - Why build the Sistine Chapel? Why research Paper but not go on to Education? Why cut off chain irrigation opportunities to get fresh water to your Farms? Horseback Riding with no Horses? - hopefully picked up as collateral in a trade. Why not build more units so your cities grow larger to the health cap rather than the happiness cap under Hereditary Rule? Why make peace with Tokugawa at this point when his best two cities were next up (I'm not sure - but it looked as though you probably could keep going)? Why only one Catapult - siege weaponry is very important once available?
Perhaps a more important one; What victory condition to you have in mind? You've got a job ahead of you if you want to take out Japan and more so Mongolia, as you're pretty weak from a military standpoint. You are behind in technology, so you'll need to play catch-up for a space race win. You have done little to nurture good relations by being the only Christian in the world, so some effort will be needed on the diplomatic front if a diplo' win by external votes is what you're wanting (easily fixable I admit by switching religions!). Rome's culture's good, but most other cities are lagging, and it's the 16th Century and still no Drama or Music, and few religions in your empire for a cultural win.
Anyway - from here I think you need to work at killing off Tokugawa. More Catapults and Macemen. Use Hereditary Rule, as indicated above, to address any happiness issues. Consider technology 'targets' on the technology tree - for instance Chemistry and Steel for Grenadiers and Cannons for taking out Mongolia once Japan's finished. From there review your victory options.
Get angry!
I know this post sounds a bit 'pick-pick-pick', but the intention is that it might be of some help!
