Doesn't Obi-Wan point out in Obsession that "every Padawan on Coruscant" knows where Anakin is spending his spare time, meaning wherever Padmé is? Although I think the CW media project had some diverging interpretations with this being the most aggressive one. And seeing how EU even kicked Palpatine down a notch - he had to find out about the wedding through Typho - I'm pretty sure Yoda and the Jedi only think of Anakin and Padmé as friends. Therefore, it's perfectly okay to constantly have them on missions together. Obi-Wan was appointed as Padmé's security in AOTC with no objection to Palpatine pointing him out as "an old friend". And what do we see all around? Jedi having "old friends" everywhere. Yoda in Best Blades and on Kashyykk, Mace with the Colossus of Destiny. Bail Organa if you look at it the other way round. The Jedi still form connections with other beings, keeping contacts so that they can effectively help on a galactically important level, not just on the level of diner owners and freighter captains. If Yoda senses anything, then only that Padmé has an important destiny, and that it is a good thing to have a Jedi with a natural connection to her. And after all, it only makes Obi-Wan more awesome if he was the only one who found out and tried to support Anakin the best he could. Awesome as a friend - other than that, this probably contributed big time to his failure as a master.