Wikipedia say Anthemius was the last western Roman emperor to actually have real power. Would or would you not agree with that?

I think I would agree. Despite failing in his major campaigns against the Vandals, he actually had the power to even begin such campaigns in the first place. He also was the last Western Emperor to be recognized by the east.

Another reason I'd agree is because the reigns of his few successors were short and/or weak:

Olybrius - Reigned for a whole 4 months.

Glycerius - He reigned for a year, and there isn't much known about his rule. He's spoken of by the bishop of Pavia Ennodius as having made "many measures for the public good", but the only law to have survived is regarding matters of church.

He also managed to prevent the invasion of Italy by the Ostrogoths, but that was accomplished through less power and more coin - a bribe and a bit of diplomacy got him to change course and go for Gaul instead. He'd later be deposed at the request of Eastern Emperor Leo I by...

Julius Nepos - Had a brief reign in Italy proper before being deposed and ruling from Dalmatia. I'll get to the person who was in charge in a moment. Nepos accomplished little during his period in both Italy and Dalmatia, going about what added up to little more than some attempts at diplomacy with the Visigoths that resulted in minor territorial changes. There were also other diplomatic talks with the Vandals, but that ended up with something along the lines of Nepos saying "I really, really don't like that you have all this Roman territory, but I can't do anything about it so...I guess it's yours."

Romulus Augustu(lu)s - Depending on who you ask, this fella doesn't qualify as an emperor as he sort of usurped the throne from Nepos. That aside, he was a child and business was run through his father, the actions of which we know little about. What we do know is that the reign lasted ~10 months, before Odoacer killed Romulus' father and exiled the boy, thus bringing us to the most commonly agreed upon end of the Western Roman Empire.

edit: Minor changes for readability