The showcase is a critical part of Scrum. It is a window in to the project for the business users and will often determine their attitude and approach to the Scrum team. Done badly, a showcase will alienate stakeholders and disrupt the team's progress.
Showcase golden rules
1. Have a dedicated showcase environment. This can be expensive (unless you are using virtual environments), but it is the only way to be sure you have a reliable showcase. Using a non-dedicated environment like a QA server often leads to unexpected behavior during the showcase.
2. Prepare the showcase at least a day in advance of the showcase meeting. Complete a dry-run through the entire demo at least 24-hours prior to the showcase meeting.
3. Prepare a showcase video as backup. This video should show everything you plan to demonstrate in the showcase. If you have any issues at all during the showcase (for example network access fails) revert to using the video.
4. Check the showcase meeting room several hours in advance of the showcase. Ensure you have suitable network access, suitable number of chairs and a suitable screen/projector/etc..
5. Be prepared for questions. It is a good idea for somebody to 'play' at being the customer during your dry-runs of the showcase. Get them to ask challenging questions.
Further to these rules, I would suggest you apply the theory that if something is difficult, do it frequently. In other words, run frequent showcases both within your team and to stakeholders until you have a rock-solid process in place.
One common problem with showcases is when the team finds it difficult to stabilize functionality as the showcase deadline approaches. This is usually an indication that the team is working in a waterfall fashion during sprints, i.e. they push testing towards the back end of the sprint. When this happens the team needs to focus on completing stories (including testing and all the other criteria you have defined as 'done').
Ideally stories should last no more than a day or two and be completed to the point where they could be included in a showcase. If stories take longer than two days, it is likely the stories are too coarse grained and need to be smaller.
Sprint showcase discipline is important. Pay attention to it and you will improve the reputation of the team and make a better product.