Abbreviating first names in the bibliography In my bibliography I use the names of the authors as they are given in the publication. Usually this will be the last name, the first name not abbreviated and second names abbreviated. However, I now have the following problems:


For some authors I only have publications with their first name abbreviated. 
Some authors have their first name abbreviated in some publications and in others not. This leads to the strange result that I have them in the bibliography with their first name abbreviated only sometimes.   


Should I try to get/use the not abbreviated first names for consistency or leave the names as they are given in the publications?
At the end of the day this all boils down to opinion and you already gave the most important argument yourself: Usually, the only way to obtain consistency is to abbreviate all first names. If you try to use unabbreviated names even when the journal doesn’t, you will eventually run into a case where you cannot find out an author’s full first name by any reasonable means.

All journals that I am aware of adhere to such a citation style, so you would be in good company abbreviating first names. Moreover, such a citation style would not arise if it would lead to any practical problems. In fact, knowing an author’s full first name rarely accelerates finding a cited publication, and if then only by a little. I cannot imagine a situation where the first name would actually be necessary to find or identify a properly cited paper – you always have page numbers or similar to resolve potential ambiguities.