So far I've only tried this class (Alchemist) in one game and that was at level 4.
Originally I was scared that this class would be incredibly over powered at this level as the damage dice and healing would be quite high. I am happy to report that this was not the case.
In fact I didn't have much luck in my game as my DM managed to pass just about every Dexterity save he rolled for the monsters, in the end I resorted to using my daggers and crossbow to at least deal some damage.
Half damage on success would be a great start for the Alchemical Fire, also maybe describe the target area a bit better. A 5 ft radius could in theory hit 9 squares but I doubt that was the intent (how much of a square must be covered to be "hit"?), the area of a large monster would probably be a more accurate description. Perhaps the area could be increased at higher levels.
Changing the Alchemical Acid to an attack roll against AC would be swell, as something that doesn't rely on a saving throw would be fun.
I also ended up rolling a lot of ones and two's for my attacks, resulting in less than the minimum damage of one of my daggers. Perhaps add something (Int modifier) to the damage or have a minimum damage equal to Artificer level?
A few more Alchemical Formula that unlock at higher level would be nice too, perhaps at 5, 7, 9 and 15 (Like the Warlock), maybe even with other Formulas as prerequisites (Like the Thunderstone to unlock the Shatter-stone). Spells to take inspiration from here could be: Grease, Stinking Cloud, Faerie Fire, Bindness/Deafness, Hold Person, Blight, Light (flare!), Shatter, Wall of Fire and Snilloc's Snowball Swarm. Either as separate formulas or as more powerful versions of the formulas that don't currently scale with level. E.G. Smoke Stick could become more like Stinking Cloud at level 9.
I agree with most people here that the Mechanical Servant doesn't really fit in very well, especially since it doesn't scale at all. Either make a dedicated Artificer Specialist for having a pet, and make it scale well, or remove it completely from the class.