1981-Movement: Nothing, I have no major quibble with the songs that were released in this time period, I prefer Ceremony and Procession (was it technically a single?) to Dreams Never End and Chosen Time, the only other songs that could have done any damage as Singles.
1983-P.C.L: Blue Monday was definitely the single to release. Age of Consent is one of their classic lost singles. Should have definitely been one, whether or not it could have done anything on the charts is open to debate but it's status as a nearly universal top 10 favorite New Order song warrants single release.
1983: Confusion-God I hate this song, couldn't they have just pulled it back and released Age of Consent, or 5 8 6 instead?
1985: Low Life: I have no idea why The Perfect Kiss did so little business. I suppose it's just one of those songs that is/was before it's time. An absolute classic and deserves inclusion. I would have released Sub Culture as well, and shelved State of the Nation in favor of Love Vigilantees a year later, but that's just me :D .
1986: Brotherhood: BLT was the obvious opening single, and although Im not a huge fan of Paradise, but i do think that it or Angel Dust would have been a nice single off this album. I prefer All Day Long, Werido, and Broken Promise to those songs, but Paradise and Angel Dust sound more radio-friendly.
1987: True Faith/1963: I much prefer 1963, which I rank alongside Age of Consent as New Order's finest moment. However which song is more radio-friendly? I think True Faith may have been, but I do think it's a tragedy what 1963 became only a b-side, should have been released later and Touched could have been released instead of the Blue Monday 1988 abomination.
1988/1989: I never agreed with the singles off of Technique. I think it would have been better to have released Round and Round in late 1988, followed by Mr. Disco or Vanishing Point (I prefer Mr. Disco but appear to be in the minority) followed by a release of Dream Attack during the summer of '89.
1993: Republic: Regret made sense as the opener. Everyone Everywhere would have been nice second single, but maybe that's me. Special needed release, it would the top song off the album, alas, maybe it didn't make too much sense as a single.
2001: Get Ready: Crystal made sense as an opener, I think At Close Range, Someone Like You, or Turn My Way should have been the other ideas. 60 MPH is bad enough as a title, even worse as single.
2004: Sirens: I would have opened with Krafty and Sirens as the Singles, and then considered Guilt or Turn as the third single.