Depends on how you speed-run it.
For starters, you are going to be importing a lower-level character into ME2. Level 60 characters (minimum 2 playthroughs or modding required) will start at level 5. Level 50-59 will start at level 3. Level 49- will start at level 2 or 1. This also means that you will not have as many points to spend on powers in ME1, including Charm/Intimidate if that is something you care about.
Speed runs will usually entail only playing the main missions, skipping a lot of the side content. The good news is that means you will skip all the driving, scanning, minerals, ID tags, data discs, and asari writings. I think the data discs give you some war assets in ME3. The asari writings can also increase some war assets in ME3 since they can help you help Conrad Verner in ME3.
Not doing any of the side missions may prevent a cameo or some extra dialogue or an email from appearing in ME2/ME3. But that is about it.
So I would say that the only real tangible effect a speedrun has is the amount of XP/levels earned in ME1 and its affect on your starting level in ME2. Personally I like finishing at level 50+ so I have a running start in ME2.