Design is in many ways about solving the visual problems that you posed for yourself.
Here I find it difficult to point to a single element and say "Don't do that!" There are some "I would never do that!"s, but my style isn't necessarily the one you desire. The problems with this poster are IMO more along the line of "Don't do this, that and those in the same poster!" You have to be consistent in your visual language. A couple of points:
The colours are strong and do clash. That's not bad per se. A poster can work with clashing colours. But it would be a bold choice. Personally I wouldn't go with such a colour scheme, but if I would, then I'd consider the colour scheme itself more than enough strain/interest to the viewer's eyes and would design the poster around non-figurative elements. Probably just rectangles, to be honest.
The textured background to me sends the message: "Designing this, I was afraid that the large background behind the simple figure might be dull. So I slapped the texture on." Either embrace the simplicity and make it stick out in your overall composition or make the texture part of the design by tastefully contrasting differently textured shapes -- probably not with this motif, though.
The hand drawn ... I don't know the English name ... at the top and bottom of the poster: Getting a "good line" is an art that takes drawing artists years or decades to master. (I certainly never did, but luckily I'm not a real drawing artist.) In addition to that, it subtly clashes with the font for "State Rhythmic Academy", which is meant to resemble hand writing, but isn't really. Either a) practice drawing lines, do several of them and then choose the best and do "State Rhythmic Academy" as real hand lettering (not recommended). Or b) do just a straight line and a straight diamond in a vector graphic programme. You already have a contrast between "flourishness" (English is not my first language ...) and geometrical straightness in the "R" of the figure: It's flourish, alluding to ancient forms of handwriting, but the line itself is uniform and done ith a computer. It makes sense to expand on that contrast. For instance, I would also try how it looks to combine your chosen font with a geometric sans-serif of similar weight and x-height.
Those are the points that stick out to me the most, without going into detaills. (I'd reconsider the balance between "State Rhythmic Academy" and the figurative element in the middle, though. Right now they fight for the top spot in the visual hierarchy, with the figurative element winning, but not by a large enough margin.) Btw., I can see that, while it's not a professional job, some thought and actual talent went into the poster.
EDIT: I just noticed that the request was specificially about background and colours. I'm not deleting my other points, though, since they are part of the overall impression. If everything else would ostensibly signal that it's a professional work, then texture and colour would come across as intentional against-the-grain choices.