Can a federal case be appealed?

I saw somewhere that the feds sometime make inmates sign a waiver of appeal if they take a plea bargain. So what if the inmate finds out later that something wasn't done legally, does this mean the inmate can not appeal and have the case reheard?Can a federal case be appealed?
It's possible, but extremely unlikely. The defendant would have to show that the plea bargain was signed under duress or that the state withheld exculpatory evidence. Not every illegality would be able to get this overturned. For instance, if there was an illegal search, that would only get the evidence thrown out, but because he confessed, they wouldn't need the evidence, so the conviction would stand.Can a federal case be appealed?
An appeal is not a rehearing of a case. It is an argument that the trial court erred in some way. Ordinarily, when one pleads guilty, that constitutes of waiver of all errors occurring before the entry of the plea. Even when no appeal is available, there are other ways of attacking a conviction after a guilty plea. Habeas corpus, a motion to withdraw the plea, a motion for a new trial. Of course, if you are successful, it unwinds the bargain and you have to stand trial on all the available charges, but that was not your question.
cases are reheard all the time when new evidence is found to exonerate the defendant