The subject of the differences between European Spanish and Latin American Spanish is a very complex one, first of all because there is no such thing as Latin American Spanish, since there are actually many variants of Latin American Spanish (for instance, Argentinean Spanish, Mexican Spanish, Chilean Spanish, etc.).
Are there differences between European Spanish and the Spanish written and spoken in the different Latin American countries? Yes, there are differences, especially at the lexical level. These differences are less notorious the higher the cultural level, but they do exist. Similarly, they are also less notorious in highly scientific texts, but again, they do exist.
There are some differences in computer terminology that are easy to pinpoint, just as there are some differences in the everyday colloquial language. There are also some expressions that are specific to only some regions.
The specific differences would also depend on the specific Latin American Spanish variant (Mexican Spanish, Argentinean Spanish, Chilean Spanish, Cuban Spanish, etc.). So, a European Spanish reader would identify a text as Latin American Spanish, but without specific knowledge of the lexical/other characteristics, s/he would probably not be able to determine whether the text was Mexican, or Argentinean, etc. A Latin American Spanish reader would also detect that that which s/he is reading is not written by a Latin American Spanish writer.
There is the concept of Neutral Spanish, which would be a form of Spanish devoid of all those (local) uses (terms, expressions, etc….) that may sound strange to any Spanish speaker.