- Is the description of the mission design tag wrong?
It is incomplete based on text snippets below and @OrganicMarble's comment. It needs to be revised to better describe what mission design entails.
- Is the trajectory design tag redundant and/or confusing and should somehow be nixed?
I don't think it needs to be nixed; trajectory design is primarily implementing $F=ma$ based on certain limits of delta-v and/or spacecraft thrust/weight ratios. Most trajectory design questions here don't address the full array of mission design concerns, and tend to be exercises in orbital mechanical mathematics and use of software.
I think that both tags are useful and complementary.
But I don't know how well they have been applied in the past or how big the current loading of incorrect tagging is.
From Chapter 7 of Integrated Design for Space Transport Systems by B. N. Suresh & K. Sivan (also google books)
Mission design is the process of utilizing the available energy for realizing the defined orbital mission by devising suitable strategies of (1) directing the energy along the suitable path, (2) sequencing the energy addition process and (3) way of utilizing the energy by shaping the energy addition process.
From Ames Mission Design Division:
Mission Design Tools and Capabilities The NASA Ames' Mission Design Center (MDC) provides concurrent engineering facilities and software for rapid mission development and analysis. The MDC is staffed by subject matter experts covering the domains required to fully develop successful spacecraft mission concepts. The MDC staff use and develop design tools supporting the full mission, including for example, orbit / trajectory design, thermal and electrical analyses, avionics and guidance, navigation and control design, development of operations concepts, and costing. The MDC facilities and staff conduct scheduled and rapid-response design cycles to develop initial mission concepts into proposal-ready, fully supportable technical packages.
From ESA's Multimedia 4: Mission design:
Satellites designed to work in unknown hostile environments are the ultimate example of ‘form follows function’: no two missions are alike.
Any initial idea needs fleshing out through the setting of solid requirements: what are all the needs of the mission to best achieve its set goal? Where will it be going in space? What instrumentation payload will it require, how much onboard power is needed and how will its results be returned to Earth?
Experts must analyse every moment of a mission’s planned journey, from understanding its destination (A comet? An asteroid? A planet?) or fixed orbit (Low-Earth orbit? Geostationary orbit? Or out into deep space?) and selecting its launch vehicle and fixing its precise lift-off time to mapping out all its planned manoeuvres. This all provides vital data for the actual design of the spacecraft and also for the mission control systems and stations on the ground.