Less factionalism would be a necessity. In the case of the navy, the Beiyang (North Sea) fleet, with its British and German made ships, refused to help the Nanyang (South Sea) fleet as the latter fought the French fleet in the Sino-French War due to their rivalry. The same with the Nanyang towards the Beiyang during the Sino-Japanese War. Cooperation between the two major fleets would do wonders to improving the Qing's naval situation and potentially prevent the Sino-Japanese War from going as badly as it did (as they'd be able to keep Japan from controlling the Yellow Sea).
Of course, part of keeping more unity (that is to say, having the country work towards a common goal rather than have the government in control of everything) is to butterfly the Taiping Rebellion (have Hong pass his exam the first time and not go crazy). It keeps the regional generals from having too much power and actually allows the Qing government to get its armies to work together to defend the country rather than gear up for a civil war (basically the Warlords Period). During the Sino-Japanese War, again, the Beiyang army was pretty much the only one fighting, despite there being armies in various other regions (unwilling to help due to their loyalties lying elsewhere).
The Qing's defeats, especially in the later years when they had actually adopted modern equipment, was more unity based than technology based. Part of it was just the ethnic part (Manchus vs Han) and part of it was regionalist/power plays by regional generals. Keep the Empire together (hard to do with a perceived foreign dynasty, the size of China, the linguistic differences between regions, and just human lust for power, but still not impossible) and it won't fall nearly as hard. After all, each new failure just set China up for the next (losing to Britain opened the country to opium, struggling with the Taiping gave the regional warlords autonomy at the cost of unity, losing to Korea, Taiwan, Liaodong, etc. to Japan, for example, set in motion the events leading up to the Xinhai Revolution).