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Save file attatched. From the save point, fortify all the units (just to make life quicker) until you get to the first ICBM (in Xiang Gang). Use this to nuke Athens (southwest corner of the eastern continent, looking very green). Fortify the remainder of the units as they become active. Watch the little auto-workers scurry around. Smile contentedly (optional). Hit space to end turn, and watch one of your battleships get sunk, and someone else's submarine. Finish researching something (I forget what) and click okay to research ecology. Click okay to all the city build popups. When you get to the end, go to Xiang Gang (up in the north, if you've forgotten), and go to the city screen. Lo and behold, there is now a bomber and a mech inf there, where previously there was only a mech inf (and the ICBM that you used). The bomber only shows up on the city screen, not the menu you get if you right click on the city on the main screen. Pick the modern armour army just to the south and move it into the city. It will (eventually) kill the mech inf. If you move out of the city if appears empty, but the city screen still shows a bomber there (clicking 'activate' on it from the city screen fails to activate anything).
I've played around with it a bit. One time I dropped a tactical nuke on the battleship NW of New York (where all the artillery are living) to take out the battleship and frigate. I then sunk the transport SW of Philadelphia (extreme SW of continent) with the battleship that wasn't in port. All other units fortified, apart from the ICBM attack on Athens. This time I saw two mech inf in Xiang Gang.
This isn't actually the reason this was saved - it was because the stack of 28 artillery was going to the peninsula NW of New York to bombard the frigate and battleship. They couldn't move there. I tried to move a modern armour army there, and if fought against an invisible defender (NOT IN THE CITY, ON THE PENINSULA). From the amount of damage the armu took, I'd guess it was an invisible mech inf (I didn't think to check whether I had lost a mech inf anywhere). A turn or two previously I had used a tactical nuke to take out 8 battleships a few tiles further north of this (first use of nuclear weapons in the game - the save file is the autosave from the start of the turn where I discovered the invisible unit - it is no longer there in the reload).
Haven't tried using my other ICBM (in a different city), or attacking any other AI cities.
I've played around with it a bit. One time I dropped a tactical nuke on the battleship NW of New York (where all the artillery are living) to take out the battleship and frigate. I then sunk the transport SW of Philadelphia (extreme SW of continent) with the battleship that wasn't in port. All other units fortified, apart from the ICBM attack on Athens. This time I saw two mech inf in Xiang Gang.
This isn't actually the reason this was saved - it was because the stack of 28 artillery was going to the peninsula NW of New York to bombard the frigate and battleship. They couldn't move there. I tried to move a modern armour army there, and if fought against an invisible defender (NOT IN THE CITY, ON THE PENINSULA). From the amount of damage the armu took, I'd guess it was an invisible mech inf (I didn't think to check whether I had lost a mech inf anywhere). A turn or two previously I had used a tactical nuke to take out 8 battleships a few tiles further north of this (first use of nuclear weapons in the game - the save file is the autosave from the start of the turn where I discovered the invisible unit - it is no longer there in the reload).
Haven't tried using my other ICBM (in a different city), or attacking any other AI cities.
Similar scenario...I launched an ICBM from a core city (founded with my settler), after which the city's defenders were not visible. As my workers were milling about on auto two of the attempted to enter said city and were promptly mowed down by a mech infantry. 
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