The DHCP errors are just the way VM handles DHCP leases, by ignoring the Hub's DHCP lease requests whilst in the RENEW state and only responding to DHCP requests when the Hub goes into the REBIND state when the Hub has to provide some validation info to obtain a DHCP lease and hence an IP address. This is a security feature and does not affect performance in any way.
The No Ranging Response received is when the Hub has not received a response from a Ranging request which the Hub sends every 30secs. This is usually due to (but not exclusive) to a bit of noise on the upstream which prevents the Ranging Request from reaching the Hub. As the ranging Requests are sent every 30secs. it is not unusual for the odd one or two to get lost in transit. As you are getting an odd T3 every 5 days or so this will be nowhere near the frequency to indicate a significant problem.It is you get a lot of T3s in short succession then you will have a problem.
The Sync Timing Synchronisation error is when the Hub doesn't receive a SYNC message which the CMTS broadcasts at least every 200ms to synchronise the Hub's and CMTS clocks. Without the clocks being in SYNC the Hub cannot lock onto the QAM clock so the Hub goes into partial service mode. If the Hub picks up the next SYNC message 200ms later then everything goes back to normal.So, as with the T3 errors the odd missing SYNC will not affect performance and shouldn't be noticeable unless you are using a real time app such as VOIP when you might notice a minor blip.
In conclusion, whilst there are errors in the logs they are not frequent enough to be service affecting.
What device did you do the direct connection with? Has it got a Gigabit NIC?