On Barney's whiteboard, the six mathematical expressions in the three equations simplify to 69 all six times.
On Barney's whiteboard you see various references to other Barney Stinson witticisms such as the Hot-Crazy Scale, his constant use of 83%, the word suit followed by an upward facing arrow, and relationships=freeways, the analogy Barney uses to describe when Robin and Ted would breakup earlier in the series
One of Barney's formulas says: CH3CH2OH=OHOHOH. CH3CH2OH is the chemical notation of alcohol.
"Tokyo Ichi", the news Channel where Robin works in Japan, means "Tokyo One". This is in reference that she isn't taken seriously, just as she was in Metro News One.
The shirt that Ted's student Betty wears when Robin visits his class is the same shirt that Robin herself wore in "Shelter Island" (S4.E.5).