Here is a summary of the comments.
1. Duplicated Vertices
The first issue, the "hidden invisible tiny faces", which this question is about, are caused by duplicated vertices. If you active the face center overlay (Center), a little dot is shown for the center of each face. You can see them in Edit mode when you active Face Selection (3) mode.
The problem is shown by the fact that there are some face centers (dots) exactly in the middle on one edge, marked yellow in the screenshot. These faces have some width but a zero-length.
The fix for this is easy. Select everything (A), and press M, and choose Merge By Distance. Additionally, you need to enable Auto Smooth to get a clean shading.
2. Holes In the Mesh
If you have activated the Face Orientation and switch view mode (Z) to Solid, you will see there are some holes in the mesh. The outside of the cube should be blue, the inside red.
You can use the F key in Edit mode to fill the holes. Use Edge Selection* (2) to select the edge.
For larger holes enable the "Mesh: F2" addon in File > Preferences. Then you can create a squad face when you just select 1 vertex in the corner. Make sure you are in Vertex Selection mode (1). Then confirm (left-click) or cancel (right-click/Esc) the drag mode after the new face is created. Doesn't matter what you click just don't accidentally move the newly created vertex.
3. Overlapping Faces
There is a large flipped red circle (N-gon) that covers the underlying mesh. I'm not sure if you need it (is it a cover with transparent material?). If you want to keep it, make sure it gets flipped (blue).
If you peek in there you will see that the walls of the round structure have 2 edge loops that overlap with the narrow outer edge of the sticking out rim. You need to fix/recreate these walls/edge loops. Then you can use (Alt)+(N), Recalculate Outside and Blender should be able to fix all the flipped faces.