Probably the most valuable use of Notability is to upgrade your Profession. [...] It is [also] worth noting that when you draw the Unsigned Message, you can attempt a Notability check (100% odds at 9 Notability) which can reward a Surprise Package on success — the same sort of one you can normally only get from a friend Giving you a Gift, which can potentially be quite profitable.

[Other than that, uses include:]

— Upgrading your Lodgings!
If you have a Reservation at the Royal Bethlehem, a Key to a Brass Embassy Guest Room, or a Lengthy Lease to Premises at the Bazaar, then when you draw their cards, you can spend a very expensive item and a great deal of Notability in order to upgrade to a new version of that Lodging that will allow you to hold FIVE cards in your hand instead of four! However, these have VERY high requirements; all require an item worth almost 1,600 Echoes, and all cost at least 8 Notability! At Christmastime, it is possible to upgrade these lodgings much more easily, and at a cost of only 3 Notability apiece, but that's outside the scope of this.

— Trading for M_____s' B___d!
You may have drawn the card "A Presumptuous Little Opportunity" by now, allowing you to exchange wine in quantity for more valuable types. The most expensive trade, "A dangerous deal", allows you to swap five Tears of the Bazaar for a single Vial of M_____s' B___d, but doing so also costs 7 points of Notability.

— Purchasing Knife-and-Candle Prize Tokens!
If you're in a great hurry to obtain more Prize Tokens in Knife-and-Candle — perhaps to purchase a Waxwail Knife — then, if you are possessed of at least one extant Prize Token and 7 Notability, you can visit the Gamekeeper's Cottage in Watchmaker's Hill to trade all your Notability, as well as your Entry in Slowcake's Exceptionals, for one Prize Token per point of Notability.

— Specializing, and driving one of your main attributes above the cap of 200!
Once you reach 200 in a main attribute, you can choose to specialize in it from the Unfinished Business storylet in its matching location (for instance, Watchmaker's Hill for Dangerous). Doing so requires that you possess a certain item depending on the attribute, and costs you 5 Notability.
After you have specialized in an attribute, you can use the Unsigned Message to trade in all your Notability in order to SET your level in that attribute to 200 plus your Notability — giving you an effective maximum of 215. Note, however, that there are still ways to lose that bonus, such as visiting the Cave of the Nadir, and any losses you incur can only be recovered by trading in the full amount of Notability again.
Please note that at present, the text for the specialization branches states that you will be able to change it "later" -- but right now, once you pick a specialization, you cannot alter it.

— Purchasing Favourable Circumstances without the use of Fate
At your Lodgings, on the "Write Letters" storylet, you can pay 7 Notability for a point of Favourable Circumstances, which will allow you to instantly draw certain cards, such as Connected cards or the Unsigned Message, from that same storylet.

John Savage wrote:

I am working feverishly toward my second point of Notability, so I will be following this thread closely!

Have you joined god's editors and a club, and gotten a sedan or landau yet? Once you do, it's easy to gain a point a week just from the polite invitations that come along.

Also, I'd be happy to take some of your scandal (no dupes please.)