What could be wrong with an Ethernet port on a black macbook? In my house is an older black macbook. If I plug it into the house ethernet with a cable, youtube videos pause and spin the throbber and other network operations are also sluggish.

If I disconnect the cable and turn on WiFi, all is well. The TimeCapsule supplying the WiFi plugins into the same hub as the aforementioned cable (though there are many more feet of wiring involved).

Is there an log on Lion that would tell me if the ethernet interface was getting errors, or getting sick?
You would normally expect better performance from a wired connection, even it it is slower on paper, so there would seem to be a problem, and it would be anywhere on the physical connection from the macbook to the internet router.  I would first check what sort of connection you have, 10 half duplex would be bad, 100 full better (1Gb full best, but I don't know if the blackbooks had gigabit ethernet).  Check this out on your switch/router and your macbook if you can.  It could be set/requested at either end of the connection.  A bad cable could force a slower auto-negotiated rate too, so try swapping it out.