ROCK/POP Randy Newman: ''Trouble in Paradise.'' (Warner Bros. 23755-1.) Randy Newman has never had difficulty receiving critical acclaim. Only with the hit ''Short People,'' however, has he received large-scale public attention. With this new record Newman may finally conquer both the critics and the public. The polished sound of the album makes it his most commercial effort, yet he has kept his humor and wit alive. The cynical ''My Life Is Good,'' about a decadent rock star bragging about his life, is vintage Newman. ''I Love L.A.'' is a song that rocks with a punchy beat, yet contains well-crafted, humorous lyrics. The album also has its serious moments, such as the songs ''Same Girl'' and ''Real Emotional Girl,'' which are a sharp contrast to much of the material on this LP. The most emotionally moving song is ''Christmas in Cape Town'' - with lyrics about a narrator's observance of suffering there. This may be one of Newman's most powerful songs ever.