I found this. Using:
galleryIntent.setType("image/*");
galleryIntent.setAction(Intent.ACTION_GET_CONTENT);
for one of the intents shows the user the option of selecting 'documents' in Android 4, which I found very confusing. Using this instead shows the 'gallery' option:
Intent pickIntent = new Intent(Intent.ACTION_PICK, MediaStore.Images.Media.EXTERNAL_CONTENT_URI);