I think this is a pretty good report, although i'd be interested if there are any CAE examiners out there who could advise you about your level.

I have been quite critical in my corrections, and the report as you wrote is certainly well written and professional sounding.

I have written quite a lot so you can understand why I have changed things - but for me most of the mistakes are very very minor.

CAE writing part.Task: a report

I study English by my own and I'm about to take the CAE exam, I did this task in 40 minutes which is more or less the time given to do this during the test. I would be grateful if anyone can correct this report! Thank you!

The task is: 
Last month you went to observe a one-day training session for new employees at your place of work in order to write a short report on it for your manager.
Write the notes you made during the session and then write a report to the manager describing what happened during the session and recommendations for improving it.

NOTES:
TOO MUCH INFORMATION GIVEN, NOT ENOUGH CHANCE TO ASK QUESTIONS.
GOOD PRESENTATION ON STRUCTURE OF COMPANY.
SOME DIDN’T UNDERSTAND THE FLEXIBLE WORKING HOURS SYSTEM.
NOT ENOUGH ON BENEFITS LIKE CAFETERIA, GYM MEMBERSHIP,ETC.
TOO LONG! SIX SEPARATED PARTS!

Answer:

REPORT FOR MAKING IMPROVEMENTS ON FUTURE TRAINING COURSES.

The aim of this report is to outline the points observed during my attendance at the/the one day one training session and to make suggestions about aspects which can be improved in the following sessions.

Activities noticed: 

On the one hand, I would point out that the presentation of the company given as an overture introduction, with videos showing many activities done by employees, was well managed and correct for the situation. On the other hand, the speech given by one member of the scientific department confused new workers as it lasted for too long and it did not allow employees the opportunity of clarifying to clarify doubts.

"Overture" sounds too literay for a technical/factual report.

In spoken English i'm sure we would say 'of clarifying' without any problems, I don't think this is a major error.

Ways to improve the sessions:

Firstly, I would recommend exemplifying demonstrating our program of flexible working hours with better methods as a great number of employees misunderstood the idea.

This is more a question of style - demonstrate WHAT (flexible working hours) THEN how (with better methods). It is NOT a serious mistake in English and I think there are native speakers who would do it.

Secondly, it would be also a good idea to seek more sponsors, this addresses would address the issue of our poor current benefits which are not enough to maintain worker satisfaction. 

(or "to keep our workers satisfied" also works. To maintain = things/machines/standards, to keep people happy/sad/interested/satisfied) It is quite a fine difference, but enough to sound strange in this situation.

Thirdly, I suggest that we divide the sessions in into at least six parts, this would mean that employees could rest for a while and return with more energy to the training.

Again, not a serious mistake.

Conclusion.

While there may be issues still to resolve, following these suggestions would mean be the a first good good first step to a better training course.

In spoken language "this would mean a good first step" probably ok, but for a written report "would mean" is a bit informal. I imagine CAE exams like things like 'adjective order' so good first step is probably important.

Again, I think this is pretty well written overall. Best of luck for your exam!