Is it necessary to send a corrigendum? Does it make my paper look ugly? I have a paper which is accepted without any minor or major revisions in a good journal (lucky me). It is fully published. Since I had no chance to revise it, many small mistakes slipped into the proof. During proofreading I tried my best to catch any mistake and correct it. But these were two problems: 1) There were too many small mistakes so at least one of them slided my attention. 2) I couldn't ask the copy-editor to remove a whole "sentence". 

If I had the chance to revise it, I would easily fix that up. But now the erroneous sentence is there in my beloved paper. It is now fully published (as online and hard copy). I am tempted to send a corrigendum on that paper, saying that the line is incorrect and should not be there. But on the other hand am afraid that it would make my paper look not-perfect or even ugly.

Do you suggest me sending a corrigendum? Or should I wait until someone notices that and writes a letter to the editor and then I answer in a reply to that letter, saying that "yes you are right, that sentence should not be there in the first place"? And if no one noticed that, I leave that error alone.

Which other ideas do you have about this?

Thanks a lot.
Given your clarifications 1, 2, and 3, I would suggest leaving it alone. 

The modern trend is for the corrigenda and the errata to be used more for "serious" stuff, and less so for "cosmetic" changes. The guideline, for example, given by the American Physiological Society is:


  if the author determines that it is scientifically necessary


While Nature uses the following definition for a corrigendum:


  Corrigendum. Notification of an important error made by the author(s) that affects the publication record or the scientific integrity of the paper, or the reputation of the authors or the journal. 


Unless the venue in which you published your work states otherwise in their publication guidelines, a stray sentence that is not factually false, does not invalidate your claims, and does not impinge on the efforts of other researchers to reproduce your work is likely not "scientifically necessary." 

Even if you insist on perfection, you should also be aware how corrigenda are viewed by other researchers in your field. If in your field the prevailing view is that corrigenda are used for "scientifically necessary" changes to your article, then you need to be prepared to answer questions about your correction in the future (usually of the form, "Why is there a corrigendum issued for your paper? Are you sure it doesn't change your conclusions?") 

Lastly, a minor point is that if you published in a journal which charges publication fees, quite often your corrigendum will come with a not-so-small price-tag also.