Due to the mostly regular correspondence between letters and sounds in Finnish, speech synthesis is relatively simple for Finnish. However, the correspondence is really between letter and phonemes, and the pronunciation of a phoneme may vary considerably. For example, if the letter h is represented by the same sound in all contexts, the result is understandable, but unnatural. For good results, the synthesis shoukd take into account the context of a letter.
The most common defect in synthesized Finnish speech—e.g. in the Acapela online synthesizer—is lack of boundary gemination, e.g. Ota se (Take it) is pronounced as written and not Otas se, as required by standard pronunciation. This is understandable, since correct pronunciation requires understanding of the words and sentence structures, as opposite to simple conversion of letters to sounds.
Another common problem is that diphthongs are often not pronounced properly. For example, Kärsämäentie (a compound of the place name Kärsämäki in genitive and the common noun tie) might be pronounced so that mä and en are separate syllables. Perhaps the reason is that many grammars describe words like mäen as twosyllabic, not counting äe as a diphthong.
Speech recognition is more difficult than speech synthesis, but it is managed relatively well in modern technology. You can test it using Google Voice Input on the Chrome browser, e.g. at www.google.com/?hl=fi or at www.google.fi.