Actually, I have found that adjustment screws can be a very good thing, especially on a student flute. Without them, any minor adjustment is made by bending the keys. This can be a very bad thing for a student to even attempt and can, over time, bend the keys and cause serious damage. I have one handmade flute without adjustment screws. It has had few problems, but when it does, I feel completely helpless. None of my students have flutes without them, nor do I recommend it.
Some companies got the brilliant idea to put the screws underneath so that you can't see them and "assume" that it is handmade. Personally, I hate this! It makes it more difficult to adjust because you have to literally hold it upside down to see what you are doing
I try to teach my students how to do minor adjustments, but this should be done VERY carefully and using extremely small movement to the screw, which will hopefully not allow for it to become too tight or too loose. It really is best to have it looked over by a trained tech every 6 months or so for adjustments. Even the slightest adjustment can cause a flute to play differently.
I have found that the major flaw with some student flutes is that the adjustment screws don't always fit correctly and tend to come out. This can be a simple fix be a trained repairman who can replace the screw itself. Or you can do what I do in this case, send it back to the manufacturer. After talking to a Gemeinhardt rep, I realized that if we don't let them know what is happening, they don't know to fix the problems. Flutes usually don't have problems until 4-6 months after purchase. At this point, the manufacturer usually does not have any contact with the buyer, one drawback of buying a factory produced flute. On the other hand, the alternative costs as much as 10 times more.