I'd say by far the project closing phase is the most neglected phase in the project lifecycle.
Because when the project is done, everyone on the project sighs relief, especially the project manager. But when the project is done with the execution phase, it doesn't mean that it's finished and should be closed. The closing (or closure) phase should not be taken lightly by the project manager, as it has, besides the logistics of administrative and contractual closures, on the most important activities in a project: "The lessons learned".
The lessons learned report should be done at this stage (although lessons learned should be gathered during all the phases of the project), and submitted then archived for future reference. The importance of the lessons learned lies not its contribution to the current project, but to future projects. Imagine running through a situation in this project, that took a lot of time to solve. If you mention this situation in the lessons learned, the next time you'll run into it, it'll be a breeze.
I believe the lessons learned should be split into 2 parts:
- Technical/Logistical lessons learned: Huge technical and logistical problems faced during the course of the project should be mentioned in this phase. This would help future projects should they experience a similar problem.
- Project Management lessons learned: In this part, the project manager must list all the problems faced from a project management perspective (while executing the project management process). Was there a problem in managing expectations? Requirements gathering? Did the project experience any scope creep? Was the project overbudget? And, of course, why?
Now to answer your last question, I don't think the impact of neglecting the closure phase has some serious effect on the current project and the resulting product or service, but doing a proper project closure can really help future projects, and consequently make the life of the project manager easier.
One last thing, celebration (and sometimes bonuses) is part of the project closure, and it should always be done, as it gives a moral boost to your exhausted team members.