Sort-cery

Mass Manipulation is honestly a terrible card for this deck, as it's a minimum cost of SIX in order to gain control of ONE creature or Planeswalker, in a deck with zero ramp and only 20 lands.
And yes, I get that Thamaturge makes it only one mana per card, but it's still 5 to cast on one target.

Solid idea (I love tinkering with mono blue), but I see a few areas that can be tweaked to help things out a bit.

As Andross says, the Manipulation combo is a cool idea, but isn't worth the cost/benefit ratio outside of stuff like commander where you're sure to have game-winning targets and lots of mana. In single player, especially legacy, you're not really likely to see the best return on investment, and the combo needs both pieces to hit with each piece being much, much less useful on its own. I also like the Thaumaturge and Icy Blast interaction, as in this build you would essentially pay U to double tap every critter opponent controls and buy yourself 2 turns. Very creative and cool interaction. However, since I'm advocating for no Mass Manipulation, it makes Thaumaturge only have 4 applicable targets, which essentially neuters the combo (as cool as it is), so I'd advise pulling both cards out as well. This frees up 12 spots (which I'll get to in a bit).

Baral's Expertise is a nice idea, but since it's a sorcery and a 5-drop, there are better versions of it that I'd recommend instead, particularly Engulf the Shore, which is cheaper and faster and synergizes PERFECTLY with this build. You don't care about your own critters being bounced, as you can replay them for nothing anyway (if they get bounced at all), and it's basically a tempo nuke for 4.

Contingency Plan and Taigam's Scheming are great in theory, as they give you what you need in the grave and keep what you need on the topdeck, but they don't actually give you even material, and they're 2-drop sorceries, which are annoying to play turns 2 and 3, as you can't do anything else. I'd instead recommend Thought Scour and Preordain, both of which give you what you need but cheaper and faster, and both retain material so you don't waste a turn and a card to make it happen. If you're got the budget, Mental Note would be good over Preordain (possibly), but they're 5 bucks a pop.

The Gifts potential is indeed good, but with mono blue budget, there's not a whole lot you can capitalize on beyond filling up your grave and fetching 4 good things and losing 2 of them. This isn't necessarily a bad thing (I like using Gifts to find a second copy of Gifts for example), but when Gifts really becomes deadly is when it's used in combo with splashed other colors or double/triple color decks. For example, running Life from the Loam, Raven's Crime, and some tech lands means you can basically make opponent discard his whole hand every turn, and opponent can't do much about it (besides grave hate stuff). While I won't advocate a complete recoloring of this build, I'll suggest a cool bit of synergy to run with Gifts that won't call for too big a rehash. If you're ok with splashing green, you can run a copy of Uro, Titan of Nature's Wrath, which you can pick up for like 3 bucks nowadays. You'll have to change your lands a bit (won't be difficult or expensive, I'll help), but it would force opponent to give you a beast of a card either way. Ideally you'd run 1 copy of Uro, 1 copy of Life from the Loam, 1 copy of Lonely Sandbar, and 1 copy of Tranquil Thicket. This will turn your deck into a self-milling machine that also nets you material every turn (4 mana turnaround gets you a minimum of +1 card and mill 3 with the Loam back in hand again (so you can keep doing it)). And the best part is, opponent can't stop the combo without grave hate, as it doesn't matter what he picks. Running that change will cost you about 10 bucks total (plus another 4 bucks to change the lands around a bit), added to the 5-10 bucks for the other changes, just to put that in perspective.

The other major changes I'd suggest would be more classic blue staples, as you get the bonus of them being cheap and helping you do what you're trying to do. Running 4 Counterspell just makes perfect sense, as being able to say 'no' when you need to is basically never a bad thing. Instead of Thaumaturge, I'd recommend either Augur of Bolas or Hard Evidence, which do nearly the same thing, but using slightly different timing and with slightly different benefits (immediate material and stronger blocker slower vs delayed material and weaker blocker immediately (+extra grave sorcery)). If you can afford it, running a few copies of Lorien Revealed would go a long way, as you can cycle it turn 1 at instant speed to fetch an island and fill your grave, and they make for good late game topdecks. Whelming Wave is another good pseudo-nuke option, although it's slower than Engulf the Shore, it doesn't touch you at all, so that's always nice.

There are a few cards considered 'generally underpowered' that I sort of like for this build too. Hithlain Knots, Remand, and Startle are all useful for stalling critter builds while filling your grave, moving you through the deck, and keeping your material healthy. Remand in particular is worth considering, as it does everything this deck wants it to do, and can essentially be read as 'on turn 2, take an extra turn (sort of)', so when you get a Remand in the opening hand, things are looking up.

A lot of thoughts, I know. But I've got a soft spot for mono blue, especially since it can't really protect itself from anything that hits the field like every other color can.