One of my first tasks at my first job was conducting placement tests, including the spoken interview; it was extremely difficult at the time and looking back, I probably shouldn’t have been assigned to do it, and this has probably shaped my views on conducting placement testing.
It’s a very good sign when a school has a well-organized placement test. Ideally, a written part should have some measurement of different skills: reading, writing, grammar, vocab and listening, and a spoken component is extremely useful too.
One school I worked for had a couple of pictures to be used with the spoken part, which was good because, while asking questions is fine, students can take cues from your questions (like which tense to use) whereas with pictures (What do you see? Describe this picture. How do you think s/he feels? Why?) it is all up to the student.
One other complication is that many students can write (or choose the correct answer) but not use the language – and this needs to be factored into their placement. It takes skill and experience not only to formulate good questions to find this out, but also to just compare their use of English to students at levels – ones you have taught!