Like any scenes that are easy to miss or any hidden quests (like Treasure chests that I shouldn't open)?
Please, no spoilers for story wise.
Fortunately you can open all chests here without worries, some of them turned into monsters but they are easy to beat and give items...
There are some long side quests like chocobo breeding, optional but if you start this on disc 1 it's a good start to collect items (common and rare ones) plus chocographs. Also try to visit all places even if it's optional (gates, qu's marsh, etc)
Remember that your abilities are far more important than raw stats in this game. All weapons and armor teach various skills and abilities and I would recommend sticking with a particular piece until you master all it has to offer, rather than just slapping on the most powerful stuff as soon as you get it.
I actually find ability mastery to be one of the most fun things about FFIX's system.
Made a new channel, come see my let's plays if you want~! http://www.youtube.com/user/themorphingfennecfox
Even though it is tempting to sell your old equipment, try to avoid doing it. A lot of it is used as components for synthesising new equipment. Most of the stuff you need for synthing can be reobtained if you do sell or otherwise lose it, but there are a few cases where you can miss out on items permanently if you get rid of what you need to make it.
Get 100/100 nobles in swordfight minigame,it gives you a moonstone(only 2 or 3 exist in game) and 10000 gil.
Spoilers which consist of nothing more than 3 locations you will visit are below
Then use those 10000 gil to buy 99 wrists in village of dali and once you get to lindblum synth 99 cotton robes,sell all except 3 or 4(they are the best armor for your mages at that moment in time),after doing this you should have plenty of money(190000+),buy 99 steepled hats and once you are on disc 2 you can repeat the process if you revisit village of dali for 99 wrists so you can synth 99 more robes in treno. After that go back to dali buy 99 more wrists and you can synth 99 more at a later date in disc 2. Doing this alone gives you around 400000 gil without even calculating random battle spoils,chocobo hot and cold gil etc. This of course is not necessary but it sets you up for the entire game more or less and is especially useful for the auction house
Inb4 vegh with his "i will never do cotton robe trick because i farm grand dragons"
That I never could do and since I got all the gil for making 99 cotton robes via level 5 deathing Grand Dragons on disc 3 I never bothered to do the cotton robe trick.
After all 60,000 gil as a profit IMHO isn't that much when it still costs 135,000 gil to make all those robes I'd rather just level 5 death Grand Dragons until every pc is at level 99 from level 40 and make more gil without spending any in return.
Besides I never won the 10,000 gil via the sword fight and after doing all possible AP farming even outside of Dali I only had enough gil for 99 Wrists but didn't have any gil left just to buy 1 copy of the other item to make the cotton robe but didn't have 2000 gil left to make 1 robe either.