Learning from checking a 9-volt battery the wrong way with a multitester
The number one thing you should have learned is how easy it is to create a short circuit with a multimeter.  Don't make the same mistake with house current -- it may turn your multimeter into a grenade!  Literally!  

Dave of EEVblog does an excellent multimeter input protection teaching on youtube (EEVblog #373 - Multimeter Input Protection Tutorial) where he explains the different levels of protection, including high rupture capacity (or HRC) fuses that should be in the current testing paths, along with the good physical shielding a quality multimeter incorporates.  In order to test current, you are creating a short circuit...

If you watch the video, and you haven't heard him say "blow your hand off", you haven't watched the video long enough.  There are certain things about electricity that we don't want to learn the hard way, so just make sure to stay with low voltage circuits while you are "burning and learning."   And invest in a high quality multimeter (it's not just about precision and accuracy -- it must have the HRC fuses -- open the multimeter up!). Fluke is a revered name in the business, and recommended.

Here is a text-searchable list of Dave's EEVblog episodes -- watching the multimeter-related episodes now would increase the profitability of your recent learning experience.  I still remember seeing multimeters blowing up, and I keep that in mind at times for my own self-protection.



EDIT:

See also:  EEVblog #94 - Near Death Multimeter Experience

FYI, with a fresh "Heavy Duty" 9-volt battery on two of my multimeters, it puts out 1 Amp.  And with a fresh "Alkaline" 9-volt battery, it puts out 5 Amps. I've experienced what you've done on other meters where the switch determines where the decimal point is and how it reads, but the numbers are otherwise correct. You likely went from 3.5 Amps down to 0.5 Amps. There's no harm in taking the same battery and, with the mode in the correct position, duplicating what you did, short-circuiting it for a few seconds and watching the current drop.  I do this all the time as a quick test of the life in a battery. Just don't let the battery get too hot -- batteries can and do explode.