The 'Captain's Log' anomaly still does absolutely nothing. I found about 8-10 of them, built out a nice medium warship and upgraded my Flagship. Total experience = 0. This anomaly has never worked, in any game. Why can't the experience just be given immediately, not supposedly awarded on an upgrade?
It IS given immediately. It just doesn't DO anything until you upgrade it.
Don't look at the experience bar. Check ship details.
I'm seeing it give +3 experience per Captain's logs anomaly, both in DA and in TA. Although I haven't updated my TA recently (though I will do so shortly), I find it difficult to believe something so simple could become broken, for any reason, and it does work in the version that I have.
This experience is given regardless of whether or not the ship has weapons; however, the experience bar does not show until the ship is upgraded into one that does.
If you've picked them up with your flagship and then upgraded it into something rather beastly, the bar may just be so small (in proportion to what is needed to level up) as for you not to notice.
Admittedly, +3 experience is pathetic, but it -does- work.