Not even close to everything.
There are seven jurors. Each is tied to an event.
- If you eat the old man's lunch, one juror will vote you guilty.
- If you run off while she's buying candy, another juror will vote you guilty.
- If you grab the pendant before speaking to Marle, another juror will vote you guilty.
- If you ask Marle to sell her pendant to Melchior (or say that you were attracted to her money in the trial), another juror will vote you guilty.
- If you do not rescue the girl's kitty, another juror will vote you guilty.
- If you speak to the little girl before rescuing her kitty, another juror will vote you guilty (this one is a sneaky jerk who catches many people unawares).
- If you deny being the one who bumped into Marle during the trial, another juror will vote you guilty.
There is no "trying" to clear Crono's name, it's completely up to you exactly what each juror does.
Also, the verdict does influence things. If you are innocent, you'll get delivered a care package. The more jurors vote innocent for you, the more Ethers it will contain. If they all vote you innocent, you get 5 Ethers, I believe.
On the other hand, if you are voted guilty, you miss two extra lines of dialogue when being transferred to the dungeons. For this reason, speedrunners make sure to be guilty because it saves time (Chrono Trigger, in addition to being one of the best games of all time, is also considered one of the best RPGs for speedrunning by the speedrunning community, because it is one of the very few where you are optimizing for speed almost constantly throughout the run).