Can mammograms detect all types of breast cancer?

Yes: Yes, however, it depends on your breast density. The more dense your breast tissue is, the increased possibility that a mass may not be seen.

Most of them: A mammogram is the screening imaging study of choice for women over 40 years old. Mammogram can pick up about 85-90% of breast cancers. In particular it can pick up many breast cancers before being palpable. Some invasive lobular cancers may be harder to be picked up. However, the mammogram is intended for detection of all breast cancers. Digital technique has ehanced the mammogram quality.

Yes: All types of breast cancer are potentially detectable mammographically, although some types(e.g. lobular carcinoma) are more difficult to detect than others.