For instance, there could be evidence that establishes a believable motive other than self-defense. There are often also non-trivial inconsistencies in the defendant's statements. A person who is truthfully asserting self-defense is typically going to give statements to police, because telling the truth keeps them from being arrested for murder. In order to appear innocent, a person falsely claiming self-defense will do the same. But it's really hard to (1) come up with a detailed story that is internally consistent and consistent with any other evidence there may be, and (2) remember every important detail you tell the police so that your story doesn't change, at least not in ways that indicate lying rather than understandable blurring of memory. (Some minor inconsistencies are expected even from a truthful person, so that's something that has to be assessed case by case. But depending on the particulars, an inconsistency can be compelling evidence of guilt.)
I think those who are claiming that the Stand Your Ground law is effectively a license to kill are mistaken. At least they are mistaken that the "stand your ground" aspect makes it significantly easier to get away with murder. Even if there's a duty to retreat, that just means that a person falsely claiming self-defense has to make sure he tells the cops he either tried to get away, or believed it would be impossible or unsafe to try to get away. Or tell a story such that no one would think retreat was an option. If there are no witnesses, there are no witnesses to dispute whether safe retreat was possible any more than to dispute whether the deceased was the aggressor.
Some of the procedural aspects of the law might make it more difficult to prosecute murders where the killer falsely claims self-defense, but even then, the procedural presumptions for those claiming self-defense will generally only be helpful in situations where the person would not be convicted anyway, guilty or not. Consider: All the prosecution has to do to get around the immunity from prosecution is to show probable cause. The presumption does not stop them from investigating, and they can question the shooter under the same rules as any suspect in any crime. If the state can show probable cause, then the defendant has the opportunity to prove by a preponderance of the evidence that it was self defense. But if there is no probable cause, or if the defendant can show by a preponderance of the evidence that it was self defense, then how on earth could the prosecution ever prove beyond a reasonable doubt that it was not self defense? So again, the immunity isn't going to protect a person who could be convicted at trial. There are no special rules unique to Florida that make the trial itself more favorable to the defense when self-defense is claimed, so the prosecution does not have to prove anything it doesn't have to prove in any self-defense case anywhere in the country. The standard of reasonable fear of death or serious bodily injury is the law everywhere in the United States. If the state can't show probable cause, or can't prove something by a preponderance of the evidence in a pretrial hearing, then they aren't going to be able to prove it beyond a reasonable doubt at trial.