Most of the badly done anime songs I've heard were in English re-dubs, though I haven't seen any of those in a while (sometimes my friends and I would get stuck with the English re-dub of Magic Knight Rayearth after the subtitled tapes sold out, and I watched the English re-dub of most of Nadia because the library didn't have subtitled VHS-later when I got a DVD player, I watched the Japanese version). The MKR theme songs were pretty awful in English, and the musical episode of Nadia (Fushigi no Umi no Nadia/Secret of Blue Water) was horrifying.
To be fair though, there are some bad ones in Japanese, too-I couldn't believe Mermaid Melody Pichi Pichi Pitch's low budget voice acting in a series where music is an important theme. The catchiness of the songs kept me watching, though. sweatdrop