How can the target change depending upon the cell type? If the gene is active for a given set of cells,the miRNA should also be capable of exhibiting its action
It happens a lot that you can't validate a published target in your cell. One of the explanations for observed differences is that distinct cell types have their own unique mRNA profiles. Since single miRNA is able to target multiple mRNAs, these mRNAs may display competition for miRNA binding sites. Thus, interpretation of specific miRNA changes depends on the cell-type specific background.
Target database as well as published datasets are all references. The most important validation lays in your systems. Most of the database will include most likely targets (again, those are predictions). If some gene was reported as a target of a miR but not in database, it may contains non-conserved type of target site. As long as it works (with validation, such as mutated site abolish targeting, etc). It should be ok.
The microRNA (and/or target) databases are important as a start point. After we need experimentally confirm if a specific association between a given microRNA and its eventual target could in fact occur into the intracellular milieu. Currently the choice method to do this is the luciferase/microRNA mimic assay.