For instance, if I really hate littering, and I somehow become
President of the United States, could I effectively make littering a
capital offense by promising to immediately pardon anyone who kills a
First this could be considered incitement as noted in this answer. Should something as explicit as this happen I would expect that swift action by congress to prevent this kind of corruption and sullying of the office. But, no, there is nothing beyond basic human decency and nearly assured repercussions to prevent it. The presumption is anyone who invests the time and money to rise to this position of power is not going to throw it all away on something like this.
Lets look at an example that is more plausible. A president has a serious bias against non Christian persons of color. That president does not explicitly promise to pardon those who commit crimes against this class of people, but starts issuing daily pardons for white Christians arrested the day prior for those crimes. There is nothing that would prevent such a thing again beyond the fact that it would destroy their career, and probably get them impeached.
Could I have my political enemies killed by promising the pardon their
Yes. Now the rub here is that your assassins have no incentive to keep their mouths shut about their actions once they are pardoned. So it is really not a great incentive to commit the crime on its own. Further while the assassin and their accomplices may be pardoned, the president would still be on the hook for the crime. And the now pardoned assassins could be off the hook by simply telling their story and complying with the investigation. Impeding the investigation or lying about the crime is likely to be the only thing that would trip them up.
If this were to come out I would expect not only that they would be impeached but that they would be arrested immediately pending criminal prosecution. While the pardon would likely be upheld it is not going to prevent the federal government from making the attempt to have the pardon annulled.
It is possible as soon as the conspiracy is revealed that the president could be arrested as well and prevented from issuing a pardon. While that detention and prevention may be later found to be illegal, it will not afford the now impeached and incarcerated former president to be able to issue those pardons retroactively.
Are there any checks and balances on the pardon other than term limits
Yes abuse of the pardon could result in impeachment. Beyond that it has been affirmed multiple times that it is the authority of the president to issue pardons without the advice and consent of either the Supreme Court, or Congress.