Compared to other countries, the Philippines may not have the budget to move to a more research-oriented academic culture (like the US) from just lecture-oriented (like Russia). Of course, the top universities constantly produce quality research output.
While the "Big Four" universities (i.e., University of the Philippines, Ateneo de Manila University, De La Salle University-Manila, University of Santo Tomas) have world-class academic standards, there is still a big gap between the top universities and the other schools (particularly the public schools). What are the best schools in the Philippines?
Not attracting enough foreign students. To be fair, some medical programs have attracted foreigners, particularly from the Middle East, but the Philippines is not yet known as the destination in Southeast Asia. The Big 4 universities have tried to encourage foreign exchange by adjusting their academic calendars (starting 2015) to make it compatible for foreign exchange programs with neighboring countries. I hope that the entire country will eventually follow this.
Potential decline of quality English. Why do Filipinos speak such strange English? This is not just a problem with the education system, but also a problem with the mass media that wants to target the majority of the population, who are economically poor. Having said that, the current fluency level of English of the Filipino population is still competitive compared to other Asian countries. Who can speak better English: Filipinos, Singaporeans, Malaysians, Hongkongers, Indonesians or Indians?
Absence of industries that support advanced specializations, such as engineering and manufacturing. The talented graduates of high-end local programs will have to work abroad to continue in that career path. I studied in a top Computer Science-Computer Engineering program in the country, which has specializations in robotics and digital signal processing, but it's almost impossible to find a relevant industry locally.
It is good that the K-12 program has been implemented and the Spanish language (a "nice to have" addition to English) was considered to be eventually re-introduced in the curriculum, but these might be difficult to implement well considering the fact that we still have to solve the existing problems: