If the basis of your appeal is that the trial court misapplied the law, you have a much better chance of prevailing than if your argument is simply that the trial court just made the wrong factual determinations. This is because the Court of Appeals is very deferential toward the trial court's findings of fact, and requires an appellant to prove not just that the trial court likely made the wrong factual determinations, but actually abused its discretion in doing so. This is called the "abuse of discretion" standard of review.
For example, if you're appealing the court's child custody award on the grounds that the trial court did not properly weigh all of the evidence when it found that the children's best interests were best served by granting primary physical custody to the other parent, because the court gave too much deference to the custody evaluator and not enough to the child's preference, etc., that is going to be a very tough sell because of the "abuse of discretion" standard.
If, however, you're appealing the custody award on the grounds that the Court applied an incorrect legal standard -- such as an "endangerment" standard instead of "best interests of the child" standard, in that case you'll have a much easier time on appeal --- assuming of course that you're correct about how the trial court misapplied the law. When the Court of Appeals decides issues of law as opposed to issues of fact, it applies a "de novo" standard of review, with no deference to the trial court.
Although you always have the right to appeal, a big impediment to the free exercise of that right is the cost. Appeals are never cheap or easy. They're a lot of work --- around 30 to 60 hours depending on the case and the issues. Multiply that by you lawyer's hourly rate, and you can see how it is simply beyond the means of many to appeal.
Recently the Minnesota Court of Appeals has started a mediation program that is specially designed for resolving appellate level issues. This is one way to potentially resolve appeal issues without prohibitive expense.
If you do want to appeal, or explore the possibility, it is important to act quickly, as the deadline for a "direct" appeal is 60 days from entry of the divorce decree.
Lastly, it is important to remember that many appellate issues cannot be heard at all unless you first bring a Motion for Amended Findings and/or a New Trial at the trial court level. The purpose of this rule, in principle, is to allow the trial court the opportunity to fix its own mistakes, so that the need to appeal may be avoided altogether in some cases. If you do not first bring a Motion for Amended Findings and/or a New Trial, then your grounds for appeal are limited to whether or not the evidence supports the trial court's findings, and whether its findings support its legal conclusions.