The human soul may be compared to gold. The more we polish an object made of gold, the brighter it gets. While a certain degree of shine may indeed be beautiful, it may be less than the maximum possible, and hence, relatively defective.
The word chet, which we generally translate as "sin" or "mistake," can also mean "a defect." The above verse can thus read, "My defect is forever before me." Since growth is an endless path, we can always strive to reach a higher level than where we are now. Therefore, we can always consider ourselves relatively "defective" in the sense that we can always find room to improve.
However, the result of such consideration should not be dejection. To the contrary, just as graduation from one level of education prepares and enables us to move to a higher level, and we are certainly not saddened by moving up, so should our awareness of our own "defectiveness," i.e. that we can reach ever-greater heights, never be a cause for sadness. Progress should bring us joy.