As I understand from the principles and parameters theory, all parameters are binary. In particular, the head directionality parameter can be set to either "head-first" or "head-last". The setting of one value or the other determines, among other things, which kind of adposition the language will have. Head-first generates prepositions (e.g. English). Head-last generates postpositions (e.g. Japanese). But Finnish is an example of language that has both prepositions and postpositions. What am I missing?
Following up on jlovegren's point that head directionality does not empirically hold:
Anders Holmberg and other researchers have been attempting to sharpen the analytical relevance of mixed order languages such as Finnish into the Final Over Final Constraint which states, paraphrased very loosely, that head-finality is restricted to positions where it only dominates head-final structures. Hence mixed order languages can have head-final configurations up to some point in the (relevant) syntactic structure, where it switches to being head-initial.
As support of this proposal, Biberauer, Holmberg, & Roberts 2010:19-21 point out the observation from Holmberg 2000 that while both postpositions and prepositions are present in Finnish, a postpositional phrase involving a complex NP is ungrammatical:
1a. ennen sotaa
`before the war'
1b. sodan jälkeen
`after the war'
2a. ennen [käyntiä [nurkan takana]]
before [visit [corner behind]]
`before the visit around the corner'
2b. *[käynnin [nurkan takana]] jälkeen
[visit [corner behind]] after
Under their analysis, (2b) is ungrammatical because it involves a head-initial NP embedded within a head-final PP.
Insofar as the status of head directionality as a binary parameter is considered to be an empirical hypothesis, it is false as an absolute universal. So you are not missing anything. Uniform head directionality, however, is a bidirectional statistical universal. VO word order is highly predictive of prepositions, and prepositions are highly predictive of VO word order. And vice versa. For data on the correlations between verb-object and noun-adposition word orders in 1142 languages, see Dryer 2011.
If, however, you would rather not reject the parametric head directionality hypothesis, you can claim that something else is going on in the languages which fail to adhere to the word order correlations. Baker and Kramer 2011, for example, argue that prepositions in Amharic (which has OV word order) are not really prepositions, but case markers. But the more you indulge in the "it's not really a post/preposition" gambit, the more strict head directionality turns into an analytical principle rather than a testable hypothesis.
This is not unique to Finnish: consider the postposition ago in English, for example.
The answer is that the assignment of parameters is not always consistent throughout a language, which is only natural since language change does exist and parameters do change with time. However, one talks about whether a language is mainly head-first or mainly head-last, so you could say the parameter is not really binary.
In the case of Finnish, postpositions are more common.