How has forensic science and other branches of science helped in our understanding of Otzi, the Iceman, especially regarding medical and botanical examinations?
Forensic science, anthropology, botanical, medical, genetic, nano and archaeological sciences examinations all contribute to the still developing revelations about and understandings of Otzi, the Iceman.
When applied to archaeology, forensic science examination is the collection of physical evidence at the archaeological site, which is then examined in a laboratory so the resulting data can be analyzed and conclusions drawn about the truths (or theorized truths) relevant to the site and events at the site.
The latest development resulting from science refutes previous studies that had indicated that no blood samples existed for Otzi. The theory was that either the blood cells had all degraded or that Otzi had bled so profusely from his fatal arrow wound that even arteries and vessels were emptied. However, in a new study using nano science technology, a "nano-sized probe" (using laser science to record images) in the two open wounds Otzi has uncovered "classic 'doughnut shaped' red blood cells," as reported in the Journal Interface and re-reported in National Geographic. The nano probe and an atomic microscope uncovered the presence of fibrin, which is produced for a short time following a wound, showing that Otzi died very quickly, not slowly as previously speculated.
Another new development resulting from DNA decoding is that Otzi's eyes were brown, not blue as previously theorized. Botanical science discloses that he wore a woven grass cape over his leather clothing and had a "woven-grass sheath" for his flint-tipped knife, which was attached to his leather utility belt. Archaeological evidence of these artifacts were found at the site where Otzi's mummified remains were found. Another artifact of great significance was his copper ax. Otzi lived in the Copper Age thus his copper-headed ax was a symbol of status and power. From this, archaeologists theorize Otzi was a "political leader" in his valley village and may have been murdered by "political rivals."
[National Geographic has an informative article, from which this answer was drawn, on these new revelations about the Otzi mummy and the 2012, in part hypothetical, Otzi exhibit.]