I feel like there's a lot of potential in his E that's not being exploited. Currently it's a major annoyance in lane, and that's about it. Since Teemo has pretty much always been about that E DOT damage, having it be a passive effect really limits his strategic play. Personally, I like the idea of turning it into a "rotating toggle", if you will. As in, each time you activate his E, you toggle between different kinds of darts that affect Teemo's auto attacks in different ways. Being able to switch between these effects would give Teemo ways to affect a teamfight that aren't simply additional damage. For balance's sake, I would suggest adding a minor mana cost to Teemo's attacks while these darts are active, something like 5 mana per attack. So the final ability would read something like this:
E - Envenomed Ammo
Cost - 5/7/9/11/13 mana per attack
Cooldown - 0.75 seconds between toggles
Teemo's darts are tipped with specialized neurotoxins that have varying effects. Activate this ability to toggle between the three of them.
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Toxic Dart (automatically active when the skill is first learned): Teemo loads his darts with corrosive poison, causing his basic attacks to deal X additional magic damage each second for 4 seconds.
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Weakening Dart: Teemo loads his darts with sedatives, causing targets damaged by his basic attacks to suffer 2/3/4/5/6% reduced movement and attack speed for 1.5 seconds. This effect stacks up to 5 times per target.
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Confounding Dart: Teemo loads his darts with hallucinogenic spores, causing confusion in his enemies. Targets damaged by Teemo's basic attacks have the resource cost (e.g. mana, fury, HP) on their non-ultimate abilities increased by 15%. If an ability does not cost any resources (e.g. Vlad's Q, Riven's.........everything), it will not be affected. Lasts 1.5 seconds.
Note that for the first toggle, the on-hit damage has been removed. This is done so that the DOT effect (which IMO has always been the primary focus of the ability) can be increased in damage while not being OP. Basically, move all of the on-hit damage to the DOT portion. Also note that with the rather short durations on the two new dart types, Teemo must constantly be auto attacking in order to proc them. However since each attack costs mana, the Teemo player must make a strategic choice about when to auto and when to save mana. This will give the opponent a reprieve in which to go on the offensive, whereas currently Teemo simply autos you no matter what, and there's nothing to take advantage of.
With his E being taken care of, I feel like the next thing to do would be to get rid of that oppressive blind. It's always been a pain in the ass for melee champs and ADCs alike, while being of little consequence to mages. In this way, it is very one-dimensional, boring, and ultimately limits his counterplay for the majority of the champion roster. Combined with his new E, I think the best thing to do is change it from a single-target nuke to an AOE cone about the same size and width as Morde's E. Reduce the ratios and base damage a bit, remove the blind entirely, and make it apply a stack of whatever dart Teemo's E is currently toggled as. So something like this:
Q - Needle Burst
Cost: unchanged
Cooldown: increased by 1 second at all ranks
Teemo draws in a deep breath and fires out a flurry of darts in a cone shape in front of him dealing X magic damage to all enemies in the area. Enemies struck are afflicted by whatever dart type his E is toggled to.
The size of the cone is debatable, but I think the sweet spot lies somewhere in between Darius's E size and Morde's E size. Perhaps make it thinner with longer range, or wider but with shorter range, depending on preference.
Honestly, I quite like his W and ult the way they are, and I don't feel the need to change them. Both are integral parts of Teemo's identity, the former making him ideal for hit-and-run skirmishes, while the later gives him vision benefits, objective control, and map pressure. All of these things are aspects of Teemo's kit that deserve to stay, and while his W may be somewhat uninteresting, and his ult the main reason everyone hates him, for better or worse Teemo was designed to be an annoying little bugger. Any rework that moves him away from this identity is bound to be a flop.