Thing's I would have written differently include TMMs, a couple pieces of equipment, and a portion of the Aerospace Fighter rules.
TMMs
I dislike the idea of units managing to regularly receiving target numbers of 11 or higher with a high portion of that being based on movement modifiers. I would cap TMMs at +4, and spread them out a bit, something like:
0-2 = +0
3-6 = +1
6-10 = +2
11-15 = +3
15+ = +4
Jumping = +1 for moving 15 or less
Now, I recognize this would probably make things a lot easier to hit, and thus severely limit the effectiveness of lighter units, particularly when opposing pilots are skilled up. To counter this somewhat I would include rules for evasive maneuvers. Evasive maneuvers would increase the target number by anywhere from 1 to 3 - choice of the pilot - while also increasing the target number of the unit making evasive maneuvers by a like amount.
Standard movement mods would remain the same, so a unit moving at safe/walking/cruising speed receives +1 penalty to hit, and max/running/etc. receives +2 penalty to hit.
Ideally this would cause a trade-off between being more offensively or defensively oriented for that particular turn, without heavily skewing things in favor of lighter or heavier units.
Equipment
There are only a couple pieces of equipment that I would change, and this is primarily due to the above TMM changes.
Pulse Lasers: Only receive a bonus to hit of -1 rather than -2. The -2 has always felt like too much to me.
TAG: Receives a bonus to hit of -2 at short range, -1 at medium range and +1 at long range, also ranges change to 6/12/21 rather than 5/10/15.
Long Ranges on ballistic and missile based weapons: Increase their long range increment by half the current spread. I'll use a gauss rifle as an example, the current base gauss rifle has a long range of 16-22, a spread of 7, half of that is 4 (rounding normally), and producing a long range of 16-26 in my modification to the rules.
Aerospace Fighters
I would change them to be a little bit more in line with how other units are built and armored, as well as slightly limit their choice of equipment.
Engines are limited to standard engines as normal in the Succession Wars eras, they are limited to lights in Clan Invasion through Jihad and Star League eras, and then in the Republic Era they start to have access to XL engines. In most advanced tech eras engines end up limited to 1 step below the best able to be used in battlemechs (and also light engines end up being developed much, much earlier than in canon).
Add a 5% tonnage internal structure, and when endo-steel becomes available allow it to cut it down to 2.5%.
And finally armor, I've always hated the idea of the "flying brick," armor should be limited to similar amounts as equivalent weight battlemechs.